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.

Question

Mathematics

Kenyon

20 September, 05:12

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.

+5

Answers (1)

Know the Answer?

Kennedi Gill · Answer 1

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.