Question

The population (in millions) of a certain island can be approximated by the function p(x)=50(1.05)^x, where x is the number of years since 2000. In which year will the population reach 200 million? Hint: An answer such as 2002.4 would represent the year 2002.
A. 2028
B. 2066
C. 2002
D. 2015

Answer 1

@kaylamarie101

Answer 2

200,000,000=50(1.05)^x
then i divided each side by 50 which gave me
4,000,000= 1.05^x
then
log_1.05 4,000,000 = x
x=311

Answer 3

after that im not sure what to do @kaylamarie101

Answer 4

Okay. give me a moment

Answer 5

sure :) Im not sure if my work is correct

Answer 6

Okay. Since you said x=311, you use the function and substitute every x as 311

Answer 7

Okay, first, you did it wrong..You but the 200 million as p(x) which is not correct

Answer 8

ahhh darn it :O

Answer 9

The purpose of this is to find out in which year the population will be 200 million. I see where you might have thought that that would be right, but let me explain it to you.

Answer 10

As an example, lets just pick on of the choices. Im going to pick 2028 because it sounds cool.

Answer 11

It says "p(x)=50(1.05)^x, where x is the number of years since 2000."

Answer 12

So, the key is seeing how many years it has been since 2000 because that will be x. So, Tell me, in 2028, how many years has it been since 2000?

Answer 13

@joanne2014 ? Can you tell me that?

Answer 14

yea im figuring it out i think

Answer 15

It is just subtraction hun. 2028-2000 will give you the difference between the two years.

Answer 16

haha i figured at the end lol its 28

Answer 17

exactly. Which means that x=28. Correct?

Answer 18

yea so then we plug 28 in for the exponent or p(x)?

Answer 19

Both. whether f(x), g(x), h(x), or p(x) when you find out what x is, you substitute the x for the number. So, in this case, x=28 and we have p(x). So:

p(28)=5(1.05)^28

Tell me what that is?

Answer 20

is it 19.6?

Answer 21

Correct! Now, is that 200 million?

Answer 22

no so i keep looking at the years until it equals 200 million right?

Answer 23

Exactly ! (: You Continue to find the difference of the year you chose and 2000 and plug that number into x :D

Answer 24

You are doing really good! :)

Answer 25

yay thankk you !

Answer 26

No problem Darlin'! I'm here when you need me!

Answer 27

And thanks for the medal!

Answer 28

Thanks for being patient :D