Question

In 1998, the population of country C was 38 million, and the exponential growth rate was 1% per year

Answer 1

Explanation:

Formula for the exponential graph is given by the function,

`P(t) = P_0(1 + r)^t`

Where
`P(t)` = population after 't' years

`P_0` = Initial population

r = rate of increase

t = Number of years

In 1988, population of a country C was 30 million.

A). Function for the population will be,

`P(t)=38(1+0.01)^t`

`=38(1.01)^t`

B). Population in year 2020,

`P(22)=38(1.01)^(22)`

= 47.30 million

C). Doubling time means the duration in which
`P_0` becomes
`2(P_0)`.

`P(t)=2P_0`

`2P_0=P_0(1.01)^t`

`(1.01)^t=2`

By taking log on both the sides of the equation,

t[log(1.01)] = log2

t =
`\frac{\text{log}(2)}{\text{log}(1.01)}`

=
`(0.30103)/(0.004321)`

t = 69.66 years