Question

A city's population, P (in thousands), can be modeled by the equation P = 130 (1.03)^x, where x is the number of years after January 1, 2000. For what value of x does the model predict that the population of the city will be the approximately 17,000.

a. 8 years
b. 9 years
c. 10 years
d. 11 years

Answer 1

log17000 = log130 +xlog1.03

Answer 2

So what's the answer or I don't get it..

Answer 3

?

Answer 4

start with
\[1700=130(1.03)^x\]
\[\frac{170}{13}=(1.03)^x\]
\[x=\frac{\ln(\frac{170}{13})}{\ln(1.03)}\]

Answer 5

now you need a calculator

Answer 6

i get 86 so i assume there is a typo in the question. is it
\[P=130(1.03)^x\] ir
\[P=1300(1.03)^x\]?

Answer 7

if it is the second one answer is 9 years

Answer 8

17000 is the population not 1700

Answer 9

Its 170,000. Sorry typo ....So it's 9 years?

Answer 10

it says P is in measured in thousands so 170000 is collapsed to 170.

P(thousands)=130*(1.03)^x

(170/130)=(1.03)^x

log(170/130)=x*log(1.03)

x= [log(170/130)/log(1.03)]

x=9.0756 years