Question

A country's population, in millions, is given by the exponential model P = 78.2e0.047t, where t represents years after 2000. What population does the model predict for the country in 2012? (Round answer to the nearest tenth.)

Answer 1

f t represents years after 2000 and you would like to know the population in the year 2012, first calculate the t value, in this case:

2012-2000 = 12

This is the only unknown number in your formula, as e is a mathematical constant that approximates 2,718.

So you formula then looks like this:
P = 78,2 * 2,718 ^ (0,047 * 12)

then:
0,047 * 12 = 0,564

which gives:
P=78,2 * 2,718 ^ 0,564

First the power function:
2,718 ^ 0,564 = 1,758......

which you then multiply with 78,2
P = 78,2 * 1,758....

Which eventually gives a population of:
P = 137,451......

Rounding it to the nearest tenth will give
P= 137,5