Question

A country's population in 1992 was 222 million.

In 2001 it was 224 million. Estimate
the population in 2004 using the exponential
growth formula. Round your answer to the
nearest million.

P = Aekt

Answer 1

@Pizza7

Answer 2

@amistre64

Answer 3

@aaronq

Answer 4

i believe kt is an exponent here?

Answer 5

yes
@amistre64

Answer 6

id just use the 2 points to define the parameters with

Answer 7

1992 was 222 million. t=0, P=222
2001 it was 224 million t=9, P=224

\[222=Ae^{0k}\]
\[224=Ae^{9k}\]
well, A has to be 222 sooo
\[224=222e^{9k}\]
log it out to find k and have a descent formula

Answer 8

does that make sense?

Answer 9

no... Im confused

Answer 10

youll have to tell me the confusion then, since this is too simple for me to dissect any further to me.

Answer 11

What do you mean to log it out?

Answer 12

we have to solve for k to find the rate at which the population is changing. e^k has an inverse. its the natural log function

Answer 13

Ok

Answer 14

this is the process i have in mind when i say log it out.

\[P=Ae^{kt}\]
\[P/A=e^{kt}\]
\[ln(P/A)=ln(e^{kt})\]
\[ln(P/A)=kt~ln(e)\]
\[ln(P/A)=kt\]
\[\frac{ln(P/A)}{t}=k\]

Answer 15

OH! ok! :)

Answer 16

:) once we know k, then its just a matter of t=12 i believe

\[P=222e^{12k}\]is our approximation

Answer 17

Thank you! :D

Answer 18

good luck :)

Answer 19

k=0.00074738916 Or 0.0007