Answer :
Answer:
[tex]4.8\%[/tex]
Step-by-step explanation:
The population that grows with an annual percentage rate compounded continuously is given by:
[tex]P=P_0e^{rt}[/tex]
The population reaches 1.1 times its previous size in 2 years.
This means that, when t=2,
[tex] P=1.1P_0[/tex]
We substitute to obtain:
[tex]1.1P_0=P_0e^{r \times 2}[/tex]
This implies that:
[tex]1.1=e^{2r }[/tex]
Take natural log to get:
[tex] ln(1.1) = 2r[/tex]
[tex]r = \frac{ ln(1.1) }{2} [/tex]
[tex]r = 0.0477[/tex]
Therefore the annual percentage rate is
[tex]4.8\%[/tex]
The annual percentage rate according to the exponential growth function is 5%
An exponential growth is in the form:
y = abˣ;
where y, x are variables, a is the initial value of y and b > 1
Let y represent the population after x years.
Let us assume that initially the population is c. hence, a = c.
The population reaches 1.1 times its previous size in 2 years:
[tex]1.1c=c(b)^2\\\\1.1=b^2\\\\2ln(b)=ln(1.1)\\\\ln(b)=0.0477\\\\b=1.05[/tex]
Hence the annual percentage rate = 1.05 - 1 = 5%
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