Question

A Country's Population In 1993 Was 204 Million. In 2000 It Was 208 Million. Estimate The Population In 2015 Using The Exponential Growth Formula. Round The Answer To The Nearest Million.

P=Ae^kt 

Answer 1

Hello and welcome to QuestionCove!

Let us take 1993 to be time "0". We can model our equation for 1993 as:
204million = Ae^k(0)
This simplifies to 204million = A*1, which also let's us solve for A=204million
7 years later in 2000, t is now equal to 7. Our A constant is still the same, and we can use our equation to solve for the k constant:
208million = 204million*e^k(7)
1.0196 = e^k(7)
log(1.0196) = k*7
0.00120426097 = k*7
k = 0.000172037281
Now we can make the full exponential equation for predicting population t number of years after 1993:
P = 204million*e^0.000172037281*t
And since 2015 is 22 years after 1993, the full equation would be:
P = 204million*e^0.000172037281*22
If you calculate that, you should get the population prediction for the year 2015

Answer 2

thank you