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anonymous
 5 years ago
what exponential function passes thru (0,4) and (2,64)
anonymous
 5 years ago
what exponential function passes thru (0,4) and (2,64)

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mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0the basic form for an exponential equation is \[y = ax^2 + b\] so I'd plug in (0,4) and we can solve for b then plug in (2,64) to solve for a

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0\[4 = 0*0^2 + b\]\[b = 4\]\[64 = a*(2)^2 + 4\]\[15 = a\] boom. plug those in your general equation (above) and you've got an answer!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0these are the choices tho 1) f(x)=4(1\4)^x 2) f(x)=4^x 3)f(x)=4(1\4)^x 4)f(x)=4(1\4)^x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thats why im confused?

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0well you can plug each set of numbers into all those functions and see which works. it looks like (1) will work for both sets.

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0ahh. i misread 'exponential' to be 'quadratic'. My answer is one example, but there are many functions that would work.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank you so much and by any chance do you know this one: 3 sides of a rectangular garden are enclosed using 120 meters of fencing. what is the maximum area of garden?

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0hmm what level math are you in? I am tempted to use derivatives, but not if you haven't learned them yet.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and yeah i havent learned that yet lol

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0well I'm thinking that the maximum area would be a perfect square rather than a rectangle, don't you think? this would mean each of the three sides are equal.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The basic form is\[y=a^{bx}\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0ok we have x+x+y=120 so y=1202x so A=xy=x(1202x)=120x2x^2 so if we find the vertex of this parabola we can find the max

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i got y=4^(3x/2) for that one

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Actually, I don't...!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so with the choices 1) 3,600m^2 2) 1,800m^2 3)1,600m^2 4)900m^2 whats the correct answer

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0anyways the vertex of that parabola is (0,120) and you find that by writing the parabole as a*(xh)^2+k where (h,k) is the vertex

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0oops one sec i made a mistake

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If you let y be length of one of the sides, and x be the length of the other two sides, then y+2x=120. The area is given by A=xy, so since y=1202x, just substitute for y in A=xy. This gives A=x(1202x). You are trying to find x that maximizes this. Since the graph of this will be an upside down parabola with roots at x=0 and x=60, this means the maximum will occur at x=30 (halfway between the roots). So the max area is A=30*(1202*30)=30*60=1800.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0When x is 0, y is 4. When x is 2, y is 64.

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0the vertex of the parabola is (30,1800) since A=2(x30)^2+1800

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Why are we talking about quadratics?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh okay so the answe is 2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[y=ae^{bx}\]When x=0, y=4, so\[4=ae^0=a\]so a=4. When x=2, y=64, so\[64=4e^{2b} \rightarrow 16=e^{2b} \rightarrow \ln 16 = 2b \rightarrow b=\frac{1}{2}\ln 16=\ln 4\]so b = ln(4). hence your equation is,\[y=4e^{(\ln 4)x }\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0you're so smart lokisan lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0haha...but wait, there's more...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[e^{(\ln4)x}=e^{\ln \frac{1}{4}x}=\left( e^{\ln \frac{1}{4}} \right)^x=\frac{1}{4^x}\]so\[y=4e^{(\ln 4)x}=4.\frac{1}{4^x}=\frac{1}{4^{x1}}=4^{1x}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So your equation can be written as,\[y=4^{1x}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lol u guys are so good at this im so confused. but okay if thats my equation whats the answer, 1 2 3 or 4

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.03600 or 1800 or 1600 or 900

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0What do you actually need to find out? I thought you just had to come up with the equation.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0imrickjames is here...haven't seen you in a while ;]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0noo .. i wrote up there earlier the choices...its asking me what the maximum area of the garden is

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay...let me check the multiple choices...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0What garden? Isn't that another question?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh, I see the garden question. So the others didn't work it out?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no i just need to answer the garden question. i need to choose one of those 4 and show work.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thanks for fanning me, Matt :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank u ..wat about if a car is purchased for 20,000. the value of the car decreases by 10% each year. about how many years will it take for the vallue of the car to reach 8,000

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0hey! you can't know it was me! heh :). impressed by your scan.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Impressed by the scan...so *that's* how I increase the fan base ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how did u get that thoo

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0These types of equations with growth and decay in proportion to themselves follow the form\[p(t)=p(0)e^{kt}\]where p(0) is the initial value and k some constant. For growth, it's positive, for decay, negative. You get this equation by solving the differential equation,\[\frac{dp}{dt}=kp\]which is separable (I don't know what level you're at). Anyway, with this equation, you use your data to find out what p(0) and k are, then answer the question.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Here, p(0) is 20,000. To find k, you know that after 1 year, the car's value is 10% less, so it's value at time t=1 is 18,000. So,\[18,000=20,000e^{k}\]Divide both sides by 20,000 and take the natural log to find k. Now you have your p(0) and your k, so you can find p(t) at any time t.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay thank uuu ! and if i have to find 3+i that equals what ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You want to find t when p(t) is 8000, so you set it up as,\[8000=20000e^{ \ln (\frac{9}{10})t}\]You have to solve for t. Divide both sides by 20,000 and again, take the natural log to find\[\frac{8000}{20000}=\ln (\frac{9}{10})t \rightarrow t =\frac{8000/20000}{\ln (9/10)} \approx 8.7yrs\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It's asking for the magnitude. The magnitude of a complex number is z is,\[z=x+iy=\sqrt{x^2+y^2}\]You consider the real and imaginary part (note, the imaginary part is NOT iy, it's y, and y is real...yi is imaginary).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[3+i=\sqrt{3^2+1^2}=\sqrt{10}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Good luck. If you have anymore questions, post them separately...I need to log out :D

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank youuuuu so muchhh
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