a Use the growth factor to determine if its graph increases faster.
B
b Use the decay factor to determine if its graph decreases faster.
C
c Use the growth factor to determine if its graph increases faster.
D
d Use the decay factor to determine if its graph decreases faster.
A
aD
B
bB
C
cA
D
dC
Practice makes perfect
a The bacterial population can be modeled by an exponential growth function. The growth factor of its function is 2.
y=a(2)^t
The graphs of exponential growth functions are increasing. There are two increasing graphs, A and D. Since the growth factor is 2, greater than the growth factor found in Part C, the graph should be steeper. Hence, the situation matches graph D.
b The value of a computer can be modeled by an exponential decay function. The decay factor of its function is 0.82.
y=a(1- 0.18)^t ⇒ y=a( 0.82)^t
The graphs of exponential decay functions are decreasing. There are two decreasing graphs, B and C. Since the decay factor is 0.82, less than the decay factor found in Part D, the graph decreases faster.
Hence, the situation matches graph B.
c The balance can be modeled by an exponential growth function. The growth factor of its function is 1.11. y=a(1- 0.11) ⇒ y=a(1.11)^t
The graphs of exponential growth functions are increasing. There are two increasing graphs, A and D. Since the growth factor is 1.11, less than the growth factor found in Part A, the graph should be flatter. Hence, the situation matches graph D.
d The amount of radioactive element can be modeled by an exponential growth function. The decay factor of its function is 0.945.
y=a(1- 0.055)^t ⇒ y=a( 0.945)^t
The graphs of exponential growth functions are increasing. There are two increasing graphs, B and C. Since the growth factor is 0.945, greater than the growth factor found in Part B, the graph should decrease slowly. Hence, the situation matches graph D.
