Answer:
The initial populations of slugs is 40
Step-by-step explanation:
we have
[tex]P(n)=40(1.156^{n})[/tex]
This is a exponential function of the form
[tex]f(x)=a(b^{x})[/tex]
where
a is the initial value (value of f(x) when the value of x is equal to zero)
b is the base
r is the rate
b=(1+r)
In this problem we have
[tex]a=40\\b=1.156\\r=b-1=1.156-1=0.156=15.6\%[/tex]
therefore
The initial populations of slugs is 40
Verify
For n=0
substitute in the function
[tex]P(0)=40(1.156^{0})[/tex]
[tex]P(0)=40(1)[/tex]
[tex]P(0)=40\ slugs[/tex]
