Respuesta :
The value of 'k' will be 0.031
Explanation
The population of a particular country was 25 million in 1984. The exponential growth function is .....
[tex]a= 25e^k^t[/tex] , where 'a' is the population in [tex]t[/tex] years after 1984.
In 1992, the population was 32 million. That means, [tex]a= 32 million[/tex] for [tex]t=8[/tex] years. So, plugging those values of 'a' and 't' into the above equation, we will get......
[tex]32=25e^8^k\\ \\ e^8^k= \frac{32}{25}[/tex]
By taking natural logarithm on both sides, we will get...
[tex]ln(e^8^k)= ln(\frac{32}{25})\\ \\ 8k*ln(e)=ln(\frac{32}{25})\\ \\ 8k= ln(\frac{32}{25})\\ \\ k= \frac{ln(\frac{32}{25})}{8}=0.03085....\\ \\ k= 0.031[/tex]
(Rounded up to three decimal places)
So, the value of 'k' is 0.031
