Question

The function f(x)=80(1.5)^x models a bacteria population after x hours. How does the average rate of change between Hours 4 and 8 compare to the average rate of change between Hours 0 and 4?

Answers:
The average rate of change is 1.5 times as fast
The average rate of change is 5.0625 times as fast
The average rate of change is 2.25 times as fast.
The average rate of change is 4 times as fast.

Answer 1

The average rate of change is 5.0625 times as fast

Just took the test. X)

Answer 2

f ( x ) = 80 * 1.5^x
f ( 0 ) = 80
f ( 4 ) = 80 * 1.5^4 = 405
f ( 8 ) = 80 * 1.5^8 = 2050.3124
The average rate of change between hours 4 and 8:
(2050.3124 - 405): 4 = 411.3281
The average rate of change between hours 0 and 4:
( 405 - 80 ) : 4 = 81.25
411.3281 : 81.25 = 5.0625
Answer:
B ) The average rate of change is 5.0625 times as fast.