Question

A countries population in 1995 was 197 million.in 2002 it was 201 million. Estimate the population in 2018 using the exponential growth formula round your answer to the nearest million

P=Ae^kt

Answer 1

210 million

Explanation:

The calculation is a little easier than that.

In the 7 years between 1995 and 2002, the population grew by a factor of 201/197. At the same rate of growth, in the next 16 years from 2002 to 2018, it is expected to grow by a factor of ...

(201/197)^(16/7)

so the population in 2018 is estimated to be ...

P = 201·(201/197)^(16/7) ≈ 210.45 ≈ 210 . . . . million

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Using the given formula, we can find the relevant parameters by filling in the given numbers and solving the resulting pair of equations.

• 197 = A·e^(k·0)
• 201 = A·e^(k·7)

The first equation gives the value of A as 197. Then the second equation gives the value of k as ...

1/7·ln(201/197) = k ≈ 0.00287160

Then for t=23, you have ...

P = 197·e^(0.00287160·23) ≈ 210.45 ≈ 210 . . . . million