4.1 Exponential functions  (Page 10/16)

The average annual population increase of a pack of wolves is 25.

A population of bacteria decreases by a factor of $\frac{1}{8}$ every $24$ hours.

The value of a coin collection has increased by $3.25\%$ annually over the last $20$ years.

For each training session, a personal trainer charges his clients $\text{\$}5$ less than the previous training session.

The height of a projectile at time $t$ is represented by the function $h(t)=-4.9t^2+18t+40.$

Which forest’s population is growing at a faster rate?

Which forest had a greater number of trees initially? By how many?

Assuming the population growth models continue to represent the growth of the forests, which forest will have a greater number of trees after $20$ years? By how many?

Assuming the population growth models continue to represent the growth of the forests, which forest will have a greater number of trees after $100$ years? By how many?

Discuss the above results from the previous four exercises. Assuming the population growth models continue to represent the growth of the forests, which forest will have the greater number of trees in the long run? Why? What are some factors that might influence the long-term validity of the exponential growth model?

$y=300{\left(1-t\right)}^5$

$y=220{\left(1.06\right)}^x$

$y=16.5{\left(1.025\right)}^{\frac{1}{x}}$

$y=11,701{\left(0.97\right)}^t$

$\left(0,6\right)$ and $(3,750)$

$\left(0,2000\right)$ and $(2,20)$

$\left(-1,\frac{3}{2}\right)$ and $\left(3,24\right)$

$\left(-2,6\right)$ and $\left(3,1\right)$

$\left(3,1\right)$ and $(5,4)$