Question

In January 2005, the population of California was 36.8 million and growing at an annual rate of 1.3%. Assume that growth
continues at the same rate.
(a) By how much will the population increase between 2005 and 2025?
By
million (to the nearest 0.001 million)
(b) By how much will the population increase between 2025 and 2045?
Ву
million (to the nearest 0.001 million)

Answer 1

Answer:

a) By 10.847 million.

b) By 14.044 million.

Step-by-step explanation:

Population, after t years:

The population after t years from the initial reference is given by the following equation:

$P(t) = P(0)(1+r)^t$

In which P(0) is the initial population.

Growing at an annual rate of 1.3%

This means that $r = 0.013$

So

$P(t) = P(0)(1+r)^t$

$P(t) = P(0)(1+0.013)^t$

$P(t) = P(0)(1.013)^t$

(a) By how much will the population increase between 2005 and 2025?

In 2005, 36.8 million, so P(0) = 36.8.

2025 is 20 years after 2005, so the population will be of

$P(20) = 36.8(1.013)^20 = 47.647$

47.647 - 36.8 = 10.847

So,

By 10.847 million.

(b) By how much will the population increase between 2025 and 2045?

In 2025, 47.647 million, so P(0) = 47.647.

2045 is 20 years after 2025, so the population will be of

$P(20) = 47.647(1.013)^20 = 61.691$

61.691 - 47.647 = 14.044

So,

By 14.044 million.