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Chapter 10: Q. 348 (page 1055)

Researchers recorded that a certain bacteria population declined from 100,000to 100in 24 hours. At this rate of decay, how many bacteria will there be in 16 hours?

Short Answer

Expert verified

The number of bacteria is997

Step by step solution

01

Given information

Given population declined from 100,000to 100in 24hours.

02

Substitute in the value for final amount and solve

Substituting, we get

A=A0ekt100=100,000e24ke24k=11000e24k=100100,000

03

Take logarithm both side and solve

Taking logarithm, we get

lne24k=ln1100024k路lne=ln11000k=124ln11000k鈮�-0.288

The equation isA=100,000e-0.288t

04

Substitute the value  and solve

Substituting, we get

A=100,000e-0.288(16)A=100,000e-4.608A鈮�997

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