Answer:
That is 74 years.
Step-by-step 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 Β is 430,000 * 3 = Β 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 Β = Β 73.8 years
Answer:
73 years
Step-by-step explanation:
Here we have an exponential function P(t) which represents the population at time t and is given by:
[tex]P(t)=Ab^t[/tex]
where [tex]t[/tex] is the time in years,
[tex]A[/tex] is the initial amount; and
[tex]b[/tex] 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:
[tex]3\times 430000=430000\times (1.015)^t[/tex]
[tex]3=(1.015)^t[/tex]
Taking log on both sides to get:
[tex]\log3=t\log1.015[/tex]
[tex]t=\dfrac{\log 3}{\log 1.015}\\\\t=73.78876233[/tex]
Therefore, it will take 73 years for the population to triple.
