anonymous
  • anonymous
Determine wether the function represents exponential growth or decay. Then find the y-intercept. 1. y=4(5/6)^x a. exponential growth;4 b. exponential decay; 4 (my choice) c. exponential growth; 0 d. exponential decay; 5 2. y=12(17/10)^x a. exponential growth; 1.7 (my choice) b. exponential decay; 1.7 c. exponential growth; 12 d. exponential decay; 12 3. y=129(1.63)^x a. exponential growth; 1.63 b. exponential decay; 1.63 c. exponential growth; 129 d. exponential decay; 129
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
For number 3 my choice was A
SolomonZelman
  • SolomonZelman
Exponential function is in the form: \(\large\color{#000000 }{ \displaystyle y(x)=a(b)^x }\) Note that, when \(\large\color{#000000 }{ \displaystyle x=0; }\) \(\large\color{#000000 }{ \displaystyle y(0)=a(b)^0=a\cdot 1=a }\) So, \(\large\color{#000000 }{ (0,a) }\) is the y-intercept of this exponential function. Also, note that if \(\large\color{#000000 }{ \displaystyle b=1; }\) \(\large\color{#000000 }{ \displaystyle y(x)=a(1)^x=a\cdot 1=a}\) THEN, this is simply a horizontal line \(\large\color{#000000 }{ \displaystyle y=a }\) And, note that if \(\large\color{#000000 }{ \displaystyle b=0; }\) \(\large\color{#000000 }{ \displaystyle y(x)=a(0)^x=a\cdot 0=0}\) THEN, this is simply a horizontal line \(\large\color{#000000 }{ \displaystyle y=0 }\) (or "x-axis). \(\Huge \color{#000000 }{ _\text{__________________________} }\)
SolomonZelman
  • SolomonZelman
And now let's see what happens if \(\large\color{#000000 }{ \displaystyle 01 }\).

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anonymous
  • anonymous
Okay i've got it so far
SolomonZelman
  • SolomonZelman
let's for instance choose b=2, and for now will stick to positive a (say a=3). \(\large\color{#000000 }{ \displaystyle y(x)=3(2)^x }\) What happens as x grows? \(\large\color{#000000 }{ \displaystyle x=1 \quad \quad y(1)=3(2)^1=3(2)=6 }\) \(\large\color{#000000 }{ \displaystyle x=2 \quad \quad y(2)=3(2)^2=3(4)=12 }\) \(\large\color{#000000 }{ \displaystyle x=3 \quad \quad y(3)=3(2)^3=3(8)=24 }\) \(\large\color{#000000 }{ \displaystyle x=4 \quad \quad y(4)=3(2)^4=3(16)=48 }\)
SolomonZelman
  • SolomonZelman
So the function keeps growing × 2 ... And you can try after this problem and choose any b and a that satisfy, a>0 b>1 and you will get that the function will grow on and on with no limit.
SolomonZelman
  • SolomonZelman
So, in fact, any time a>0 b>1 then \(y(x)=a(b)^x\) is EXPONENTIAL GROWTH, with y-intercept at y=a
SolomonZelman
  • SolomonZelman
Now, if 0
SolomonZelman
  • SolomonZelman
So the function keeps decaying and it will approach zero closer and closer the bigger x-value we plug into the function.
SolomonZelman
  • SolomonZelman
So, you can probably tell that when \(00) the function is going to decay... (called "exponential decay") and as I showed in the beginning, the y-intercept is (still) y=a.
SolomonZelman
  • SolomonZelman
Bottom line: \(\large\color{#000000 }{ \displaystyle y(x)=a(b)^x }\) y-intercept: y=a _______________________ ■ If b>1, the function is "exponential growth". ■ If 0
SolomonZelman
  • SolomonZelman
your y-intercepts in #2 AND #3 are incorrect.
anonymous
  • anonymous
They are both C if I am thinking correctly?
anonymous
  • anonymous
@SolomonZelman That was really helpful thank you
SolomonZelman
  • SolomonZelman
yes, #2 and #3 are both C, and #1 --> B was correct....
SolomonZelman
  • SolomonZelman
So, B, C, C; respectively.
SolomonZelman
  • SolomonZelman
good luck!
anonymous
  • anonymous
Thank you so much! @SolomonZelman

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