An exponential growth function is of the form \(\displaystyle{y}={a}{\left({b}\right)}^{{x}}\) where aa is the initial amount and bb is the growth factor.

If the initial population is 4 tribbles, then a=4.

If the population is growing at a rate of 50% every hour, then the growth factor is b=100%+50%=150%=1.5.

The exponential growth function is then y=4(1.5)x.

If the initial population is 4 tribbles, then a=4.

If the population is growing at a rate of 50% every hour, then the growth factor is b=100%+50%=150%=1.5.

The exponential growth function is then y=4(1.5)x.