Question

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A certain kind of bacteria multiplies at a rate of 150 percent per hour. When a person’s blood has 45,000,000 of these bacteria, the person will fall sick. Let’s suppose 100 such bacteria entered a person’s blood. How many hours will it take for the person to become sick? Arrange the steps in the right order to show how to find the number of hours it will take for the person to fall sick.

Answer 1

The steps arranged in the right order are:

45,000,000 = $100(1 + 1.5)^{t}$

45,000,000 = $100(2.5)^{t}$

450,000 = $(2.5)^{t}$

log 450,000 = log $(2.5)^{t}$

log 450,000 = log t (2.5)

$\frac{log 450,000}{log 2.5} = t$

5.632 / 0.3979 = t

t = 14.21 hours

What are the correct steps?

The equation that can be used to represent the growth rate of the bacteria is an exponential equation. The form of exponential equations is:

FV = P(1 + r)^t

Where:

• FV = future value of the bacteria
• PV = present population
• r = rate of increase

• t = number of hours

45,000,000 = 100( 2.5)^t

t = log 450,000 / log 2.5

t = 14.21 hours

To learn more about exponential equations, please check: https://brainly.com/question/26331578

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