Question

Pleasee Helpp? D:
Jessica has been tracking the population of a town. The population was 8,230 last year and has been increasing by 1.25 times each year. How can Jessica develop a function to model this?

f(x) = (8230 • 1.25)x where 1.25 is the rate of growth

f(x) = 8230(1.25)x where 1.25 is the rate of growth

f(x) = 1.25(8230)x where 8230 is the rate of growth

f(x) = 8230(x)1.25 where 8230 is the rate of growth

Answer 1

f(x) = 8230(1.25)x where 1.25 is the rate of growth
im positive

Answer 2

can you explain how to get the answer?

Answer 3

@hartnn can you explain for me?

Answer 4

Apologies! This is an exponential growth situation, not a linear one.

Assume that last year was Year 0. Then the initial value of the population was 8230, period.

Now, some questions for you:

Please evalute 1.25^0, 1.25^1 and 1.25^2. Then we'll get back to our discussion.

Answer 5

Please note that 1.25^2 signifies \[1.25^{2}\]

and that if you choose not to use Equation Editor, please write that as 1.25^2.

Answer 6

@Jessicaa : no further interest in solving this problem?

Answer 7

1.25^0=1
1.25^1=1.25
1.25^2=1.5625
are my answers

Answer 8

thanks. that's absolutely right.
Notice that every value of 1.25^x is obtained by multiplying the previous one by 1.25. Does this make sense?
You've typed 1.25^2=1.5625, which is correct;
the next power of 1.25 is 1.5625*1.25. Right?

This is why I label this problem an "exponential model."

Answer 9

Yes I understand what you're saying now

Answer 10

And note that 1.5625*1.25 is the same as 1.25^3.

So, your initial value for the population is 8230 and your common multiple is 1.25, and your exponent is simply x, the number of years in question.

You set x= {0, 1, 2, 3, 4, ... }.

So, which of the answer choices is the correct one to describe what we've discussed here?

Answer 11

f(x) = 8230(1.25)^x where 1.25 is the rate of growth right?

Answer 12

Be really careful about typing 1.25x here; that means "1.25 times x," which is inappropriate in this problem.

That's why I emphasized writing this expression as 1.25^x. " ^ " signifies exponentiation.

Answer 13

Yes, that's great. Looks like you've really come to understand this problem well.

Answer 14

Yes. Thank you so much!

Answer 15

My great pleasure! See you again.