Question

This one got me really confused :(
A country's population in 1995 was 228 million. In 2001 it was 230 million. Estimate the population in 2010 using the exponential growth formula. Round your answer to the nearest million.

Answer 1

\[A_0e^{kt}\]

Answer 2

1995 -->0
2001 -->6

\[228e^{k6}=230\]
sove for k

Answer 3

do you need help solving for k?

Answer 4

hello again and hello imranmeah!

Answer 5

morning

Answer 6

don't know why all math teachers insist on doing this the hard way.

Answer 7

first set up the equation, then solve for k, then go back and plug in the numbers. there is really an easier way to do this, but i guess if you have to do it the hard we then we can do it

Answer 8

I know, i want it the easy way :(

Answer 9

well then as imran said, the growth took place over 6 years. started at 228, ended at 230

Answer 10

so we take
\[230\div 228=\frac{115}{114}\] not a nice number but we work with it because we are going to need a calculator anyway.

Answer 11

formula is
\[228\times (\frac{115}{114})^{\frac{t}{6}}\]

Answer 12

and since 2010 is 15 years after 1995 we want
\[228\times (\frac{115}{114})^{\frac{15}{6}}\]

Answer 13

that is the answer. we can do it the other way if you like. it is longer and gets the same answer, but this method is more precise because we will not round as you do when you find "k"

Answer 14

Where did the 15 come from?

Answer 15

start at 1995 yes? and want the population in 2010. that is 15 years later

Answer 16

or think of it like this. we don't want to compute with 1995, 2001, and 2010. we started at 1995 so make that 0. then 2001 is 6 (6 years later) and 2010 is 15 (15 years later)