Answer:
Hence, it will take about 73 years for the population to triple.
Step-by-step explanation:
For this case we have an exponential function P(t) which represents the population at time 't' ; which is given as:
i.e. the equation is represented of the form:
[tex]P(t)=Ab^t[/tex]
Where,
A: initial amount ( Here we have A=430000)
b: growth rate (Here we have b=1.015)
t: time in years.
As the population has to triple over the time.
Hence, Substituting values we have:
[tex]3\times 430000=430000\times (1.015)^t[/tex]
⇒ [tex]3=(1.015)^t[/tex]
Taking logarithmic function on both side we have:
[tex]\log3=t\log1.015[/tex]
( Since [tex]\log m^n=n \log m[/tex] )
⇒ [tex]t=\dfrac{\log 3}{\log 1.015}\\\\t=73.78876233[/tex]
Hence, It will take for the population to triple about:
t = 73 years
