Question

If the population of a country increases at a rate of 1.5% annually and its current population is 430,000, how many years will it take for the population to triple?

Answer 1

That is 74 years.

Explanation:

1.5% = 0.015.

The equation for the rate of growth is P = 430,000(1.015)^n where n is the number of years.

Triple the population is 430,000 * 3 = 1,290,000, so:

1,290,000 = 430,000(1.015)^n

(1.015)^n = 1290,000 / 430,000 = 3

Taking logs of both sides:

n log 1.015 = log 3

n = log 3 / log 1.015 = 73.8 years

Answer 2

73 years

Explanation:

Here we have an exponential function P(t) which represents the population at time t and is given by:

`P(t)=Ab^t`

where
`t` is the time in years,

`A` is the initial amount; and

`b` is the growth rate.

Finding the number of years it will take to triple the population by substituting the given values in the above formula to get:

`3* 430000=430000* (1.015)^t`

`3=(1.015)^t`

Taking log on both sides to get:

`\log3=t\log1.015`

`t=(\log 3)/(\log 1.015)\\\\t=73.78876233`

Therefore, it will take 73 years for the population to triple.