Question

The formula A = 118e0.024t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 140 thousand?
A. 2008
B. 2005
C. 2006
D. 2007
@ganeshie8

Answer 1

@satellite73

Answer 2

hello

Answer 3

Hey

Answer 4

set \(118e^{.024t}=140\) and solve for \(t\)
it takes three steps

Answer 5

first step it to divide by \(118\) to get
\[e^{.024t}=\frac{140}{118}=\frac{70}{59}\]

Answer 6

second step it to write in equivalent exponential form as
\[.024t=\ln(\frac{70}{59})\]

Answer 7

then divide the result by \(.024\) to get
\[t=\frac{\ln(\frac{70}{49})}{.024}\]
i guess the next step is to use a calculator to find that number

Answer 8

looks like it is about \(7\)
http://www.wolframalpha.com/input/?i=ln%2870%2F59%29%2F.024

Answer 9

except the last bit should be \[t = \frac{\ln(\frac{70}{59})}{0.024}\]not \(49\) in the denominator as a finger slip put it in the previous post.

Answer 10

and 7 years after 1998 is ...
oh typo sorry good catch @whpalmer4

Answer 11

Makes a big difference in the result if you use 49!

Answer 12

i am sure

Answer 13

Would the answer be B?

Answer 14

is 2005 a choice?

Answer 15

Yes. That's answer B.

Answer 16

ok pick that one
hope the steps were more or less clear

Answer 17

They were. Thank you!