Respuesta :
Answer: 1) After 17.673 years ( Approx) the population will be doubled.
2) After 53.019 years the population will be 80.
Step-by-step explanation:
1) Let x represents the number of years after which the population will doubled,
Since rate of interest = 4%
And, initial number of fish = 10,
Hence the fish after x years = [tex]10(1+\frac{4}{100})^x =10(1+0.04)^x =10(1.04)^x[/tex]
⇒ [tex]10(1.04)^x = 20[/tex]
⇒ [tex](1.04)^x = 2[/tex]
⇒ [tex]x log (1.04) = log(2)[/tex]
⇒ [tex]x = \frac{log(2)}{log(1.04)}=17.6729877\approx 17.673[/tex]
Hence, After 17.673 years ( Approx) the population will be doubled.
2) Let after y years the population will be 80.
⇒ [tex]10(1.04)^x = 80[/tex]
⇒ [tex](1.04)^x = 8[/tex]
⇒ [tex]x log (1.04) = log(8)[/tex]
⇒ [tex]x = \frac{log(8)}{log(1.04)}=53.0189631\approx 53.019[/tex]
Hence, After 53.019 years the population will be 80.
