Write an exponential function of continuous growth, with an initial amount of 120 and an annual growth rate of 7%.
Hint
Use the shampoo equation. Write this function in the form of f(x) = Pert. Remember the initial amount is P.
Answer
f(x) = 120e0.07t
Example 2
Find f(5) in the function f(x) = 120e0.07t.
Hint
Easy sauce. Substitute a 5 in for the t.
Answer
x ≈ 170.288
Example 3
What famous limit does the ex represent?
Hint
It was math's old friend, Euler.
Answer
Example 4
What type of growth does the ex function represent?
Hint
There are no coffee breaks.
Answer
Continuous growth.
Example 5
Find the population of The Shmoop Coop, a large free-range chicken house that starts with a meager 50,000 chickens and has continuous growth rate of 12% over a period of 2 years.
Hint
The initial population is 50000 and the rate is 0.12 (use the PERT equation).
