Answer:
The time it will take the population to grow to 800 insects is 17 days.
Step-by-step explanation:
The growth function of the insects is exponential.
The exponential growth function is:
[tex]y=a(1+r)^{t}[/tex]
Here,
y = final value
a = initial value
r = growth rate
t = time taken
It is provided that there were 270 insects after 9 days and initially there were 80 insects.
Compute the value of r as follows:
[tex]y=a(1+r)^{t}\\\\270=80(1+r)^{9}\\\\3.375=(1+r)^{9}\\\\\ln(3.375)=9\cdot \ln(1+r)\\\\0.135155=\ln(1+r)\\\\1+r=1.14471\\\\r=0.145[/tex]
Now, compute the time it will take the population to grow to 800 insects as follows:
[tex]800=80(1+0.145)^{t}\\\\10=(1.145)^{t}\\\\\ln(10)=t\cdot \ln(1.145)\\\\t=17.00522\\\\t\approx 17[/tex]
Thus, the time it will take the population to grow to 800 insects is 17 days.
