Question

A Growing City: The population of a city grows at a rate of 5 percent per year. The population in 1990 was 400,000. In what year will the population reach 1 million?

Answer 1

F=P(1+r)^t
F: final population
P: initial population
r: rate
t: time

Answer 2

wait i need step cuz so far i did the exponential growth

Answer 3

Ignore nincompoop. This is not linear growth.

Answer 4

which is 791972.6398

Answer 5

\[10^{6}=4\times 10^{5}(1+0.05)^{x}\]
where x is the number of years from 1990. Solve the equation for x.

Answer 6

a. What is the predicted population in the year 2004? 791972.6398

Answer 7

sorry the preceding was included as well

Answer 8

i have no clue how to get the 1 million

Answer 9

im wondering if i use logs in this

Answer 10

@yomamabf Have you checked my equation. BTY one million is\[10^{6}\]

Answer 11

@yomamabf Yes, I solved it using logs.

Answer 12

yes but i dont think u applied the recent post ... oh u did ok lemme try and tell me if im correct

Answer 13

Sure. I'll wait.

Answer 14

actually im really bad at logs and cant figure this out can u explain the steps to me

Answer 15

log=log400,000(1+.05)^600,000

Answer 16

? im not good at logs

Answer 17

\[10^{6}=4\times 10^{5}(1.05)^{x}\]
\[(1.05)^{x}=\frac{10^{6}}{4\times 10^{5}}=2.5\]
\[(1.05)^{x}=2.5\]
Can you take the logs of both sides of the last equation?

Answer 18

where do u get the 6 from for the power

Answer 19

thats the million right

Answer 20

man im so lost crap

Answer 21

y is the x blank for the exponent

Answer 22

X is the number of years from 1990 for the population to increase from 400,000 to 1,000,000.\[(1.05)^{x}=2.5\]
Taking logs of both sides:
\[x \times \ln 1.05=\ln 2.5\]
\[x=\frac{\ln 2.5}{\ln 1.05}\]

Answer 23

=( where did the 2.5 come from

Answer 24

Check back on my previous posts. 2.5 is the ratio of 1 million to 400,000:
\[\frac{10^{6}}{4\times 10^{5}}=2.5\]

Answer 25

oh i see what u did u broke down the 400,000... oh ok

Answer 26

oh ok then u divide that by the 1.05

Answer 27

You divide the natural log of 2.5 by the natural log of 1.05 to find x:\[x=\frac{\ln 2.5}{\ln 1.05}\]

Answer 28

2.38095

Answer 29

the answer is "in between 2008 and 2009" btw

Answer 30

No. You have just found 2.5/1.05. You need to use the 'ln' key on a calculator.

Answer 31

.8675?

Answer 32

im supposed to use excel for these problems not a calculator =(

Answer 33

im seriously havin a hard time understanding this

Answer 34

x = 18.78 years. If you add 18.78 to 1990 what year do you get?

Answer 35

2008 i would so not be able to do a similar problem on my own

Answer 36

so is there no easier way to do this?

Answer 37

I just checked on my Excel. LN returns the natural logarithm.

Answer 38

sorry just reviewing everything u posted

Answer 39

You can also use ordinary logs (logs to base 10). The answer is exactly the same.

Answer 40

ok thank u

Answer 41

You're welcome :)