Question

The population of country A was 40 million in the year 2000 and has grown continually in the years

following. The population P, in millions, of the country t years after 2000 can be modeled by the function
P(t) = 40e0.027, where t > 0.
For another country, country B, the population M, in millions, t years after 2000 can be modeled by the
function M(t) = 35e0.042t, where t≥ 0.
Based on the models, what year will be the first year in which the population of country B will be greater
than the population of country A?

Answer 1

Answer:check explanation

Explanation:

We would apply the formula for exponential growth which is expressed as

y = b(1 + r)^ t

Where

y represents the population after t years.

t represents the number of years.

b represents the initial population.

r represents rate of growth.

From the information given,

b = 40 × 10^6

r = 2.7% = 2.7/100 = 0.027

a) Therefore, exponential model for the population P after t years is

P = 40 × 10^6(1 + 0.027)^t

P = 40 × 10^6(1.027)^t

b) t = 2020 - 2000 = 20 years

P = 40 × 10^6(1.027)^20

P = 68150471

c) when P = 90 × 10^6

90 × 10^6 = 40 × 10^6(1.027)^t

90 × 10^6/40 × 10^6 = (1.027)^t

2.25 = (1.027)^t

Taking log of both sides to base 10

Log 2.25 = log1.027^t = tlog1.027

0.352 = t × 0.01157

t = 0.352/0.01157 = 30.4 years