Question

Need serious help on this one.

An initial population of 655 quail increases at an annual rate of 18%. Write an exponential function to model the quail population.

Answer 1

General formula for this is
\[P(t)=b⋅g^t\]where P is the population at time t,
b is the population at the beginning (t=0) and g is the growing factor.

I'd say b = 655.
Do you know how to get from 18% increase per year to the growing factor per year?

Answer 2

why not just use the compound interest formula

A = P(1 + r/100)^t

\[A = 665(1 + \frac{18}{100})^t\]

Answer 3

Well that is just the same as realising that 18% increase means you now have 110%+18%=118%.
So the amount is multiplied with 1.18, making the formula:\[P(t)=655 \cdot 1.18^t\]

In the end, it's all the same...