One of the special characteristics of any exponential growth function y = Abt
is its doubling time—the time needed for the quantity to double in size. This depends only on the growth rate (or the growth factor), but not on the value of the independent variable t. As you discovered in Problem 19 of Section 5.1, this is not the case with linear functions. We now examine power functions,
y = Atp.
(a)
Consider the power function
y = 10t 2.
How much must t increase for y to double when
t = 1?

Incorrect: Your answer is incorrect.
How much must t increase for y to double when
t = 2?

Incorrect: Your answer is incorrect.
How much must t increase for y to double when
t = 3?

Does the doubling time for this power function depend only on the parameters A and/or p?
The doubling time is dependent only on p.
The doubling time is dependent only on A.
The doubling time depends both on the parameter A and the independent variable t.
The doubling time depends both on the parameter p and the independent variable t.
The doubling time depends on both parameters A and p.
Correct: Your answer is correct.
(b)
Find a formula for the doubling time DT for this power function in terms of the variable t.
DT =

(c)
Consider the power function
y = At p.
Find a formula for its doubling time involving the parameters A and p and the variable t.
DT =