Given:
Initial population = 4 millions
Growth rate = 7% = 0.07
Present population = 16 millions
To find:
The time it will take for this invasive population to grow from 4 million cane toads to 16 million cane toads.
Solution:
The exponential growth model is
[tex]P=P_0(1+r)^t[/tex]
where, P is present population, [tex]P_0[/tex] is iniital population, r is growth rate and t is time in years.
Substitute P=16, [tex]P_0=4[/tex] and r=0.07, we get
[tex]16=4(1+0.07)^t[/tex]
Divide both sides by 4.
[tex]4=(1.07)^t[/tex]
Taking log on both sides.
[tex]\log 4=\log (1.07)^t[/tex]
[tex]\log 4=t\log (1.07)[/tex] [tex][\because \log x^n=n\log x][/tex]
[tex]\dfrac{\log 4}{\log (1.07)}=t[/tex]
[tex]t=20.4895367[/tex]
Approx the value to the next integer.
[tex]t\approx 21[/tex]
Therefore, the required number of years is 21.
