A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
HELP?!
anonymous
 one year ago
HELP?!

This Question is Closed

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1How do you show growth?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1For example, if the growth is a certain percentage each year, what equation shows growth?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Let's say the growth is 10%. Since 100% + 10% = 110% = 1.1, then each year, multiply the previous year's amount by 1.1 Year 0 a Year 1 1.1a Year 2 1.1(1.1a) = 1.1^2 * a Year 3 1.1(1.1^2)a) = 1.1^3 * a Year x 1.1^x * a

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1In your case, the growth is 20%, so we use 1.2 Neighborhood A \(y = 30 \times 1.2^x\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and I would just replace x with 5?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1In Neighborhood B, you start with 45 and the growth is linear, so its: Year 0 45 houses Year 1 45 + 3 * 1 Year 2 45 + 3 * 2 Year 4 45 + 3 * 3 etc. Year x 45 + 3 * x \(y = 45 + 3x\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Part A. Neighborhood A. \(y = 30 \times 1.2^x\) Neighborhood B. \(y = 45 + 3x\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Part B. Let x equal 5 in each of the two functions above to find the number of homes in the two neighborhoods after 5 years.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Part C. Set the two functions equal and solve for x.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so y=30*1.2^5 and y=45+3(5) for B?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Yes, and evaluate each expression.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Notice that Neighborhood A started with 30 homes and B with 45. By year 5, Neighborhood A already has more homes than B. This gives you a hint as to the solution of part C.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what would I set my function equal to?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would I make a function table and use the formula until I get the same number of houses?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(30 \times 1.2^x = 45 + 3x\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohhh ok... and so that's all I need for part c, is to solve that?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1You can use a table. The hint I mentioned above is that since by year 5, Neighborhood A already has more homes than Neighborhood B, that means the year they have the same number of homes is between years 0 and 5.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Yes, up need to solve the equation, but your idea of letting x = 1, 2, 3, 4, 5 is good.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Make a table and see when Neighborhood A overtakes B.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0awee yes I get it now

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Are you given choices?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no it's open response

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm making a table rn

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1OK. Then do what you mentioned above. Make a table.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1We already know this: dw:1438567229776:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1It happens between year 3 and year 4. dw:1438567359681:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok thanks for that because I was plugging in the different numbers and didn't see when they were equal, I didn't know that it could be in between years. So it would be after approximately 3 and a half yrs?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1The smallest difference between A and B is at 3.3 years, so that is a close approximation. dw:1438567705900:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Your guess of approximately 3.5 years is also good.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh my gosh! You were more than helpful and I honestly understand and appreciate everything you've told me. Thank you sooooo much!!! If I were there I'd give you a hug! Absolute lifesaver!!!

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1You are very welcome. I just want to mention one point. I don't know if you've learned logarithms yet. Usually, when you have an equation with a variable in the exponent, you use logarithms to find the solution. In this case, the equation we had does not lend itself to taking logarithms of both sides and simplifying easily. That is why I recommended you use a table with values (which was your idea) to see when the functions are of equal value to then see at which time the number of homes are the same.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You are correct, I have not learned logarithms yet, but I will remember your advice.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.