Answer:
The value of k is 0.448.
Step-by-step explanation:
Given the exponential growth function is
[tex]A=23e^{kt}[/tex]
A= The population of the country
k= growth rate.
The population of the country increased by 10 million in 13 years after 1982.
Then the population is =(23+13)million = 36 million.
Here,
A= 36 million, t= 13
[tex]A=23e^{kt}[/tex]
[tex]\Rightarrow 36=23e^{13k}[/tex]
[tex]\Rightarrow e^{13k}=\frac{36}{23}[/tex]
Taking ln function both sides
[tex]\Rightarrow ln|e^{13k}|=ln|\frac{36}{23}|[/tex]
[tex]\Rightarrow {13k}=ln|\frac{36}{23}|[/tex]
[tex]\Rightarrow {k}=\frac{ln|\frac{36}{23}|}{13}[/tex]
[tex]\Rightarrow k=0.448[/tex]
The value of k is 0.448.
