Question

Please help with precal problem?

The population of the world was 5.7 billion in 1995 and increases according to the exponential growth model where the growth rate is assumed to be 2%. When will the population double?
P(t) = P₁ (1+r)t

A) 2012
B) 2027
C) 2029
D) 2030
E) None of these

Answer 1

D) 2030

Explanation:

You want to know when the population will double from its value in 1995 if it increases at 2% per year.

Multiplier

The multiplier for t years is given as (1 +r)^t. We want to find t such that this value is 2 when r = 0.02.

2 = 1.02^t

log(2) = t·log(1.02)

t = log(2)/log(1.02) ≈ 35.003

The year the population doubles will be ...

1995 + 35.003 = 2030.003

The population will double in year 2030, choice D.

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