Answer:
1730
Step-by-step explanation:
The exponential function is of the form
y = a × [tex]b^{n}[/tex]
where y is the insect population and n the number of weeks
a and b have to be found by using values from the table.
Using (0, 20), then
20 = a × [tex]b^{0}[/tex] ⇒ a = 20
Using (1, 30), then
30 = 20 × [tex]b^{1}[/tex] ⇒ b = [tex]\frac{30}{20}[/tex] = 1.5
Hence
y = 20 × [tex]1.5^{n}[/tex] ← exponential function
When n = 11
y = 20 × [tex]1.5^{11}[/tex] ≈ 1730 ( nearest whole number )
