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.
45,000,000 = 100(1 + 1.5)t
450,000 = (2.5)t
log 450,000 = t log(2.5)
45,000,000 = 100(2.5)t

log 450,000 = log(2.50)t

14.21 hours = t

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Answer 1

The correct order of steps is as follows:

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

→45,000,000=100(2.5)^t

→450,000=(2.5)^t

→log(450,000)=t⋅log(2.5)→t≈14.21 hours

To find the number of hours it will take for the person to become sick based on the given information about bacterial growth, you can arrange the steps in the following order:

45,000,000=100(1+1.5)

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

(This is equivalent to the first equation after simplification.)

450,000=(2.5)^t

(Divide both sides of the equation by 100.)

log(450,000)=t⋅log(2.5) (Take the logarithm of both sides to solve

t≈14.21 hours (Divide both sides by log(2.5) to solve for t).

So, the correct order of steps is as follows:

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

→45,000,000=100(2.5)^t

→450,000=(2.5)^t

→log(450,000)=t⋅log(2.5)→t≈14.21 hours

Answer 2

Step-by-step explanation:14 hrs 12 minutes

Given that a certain kind of bacteria multiplies at a rate of 150 percent per hour.

Initial bacteria = 100

Growth is 150% hence P(t) = no of bacteria present at time t is exponential as

A person will fall sick if the number of bacteria is 45,000,000

i.e.

Take log on both sides

i.e. in 14 hours and 12 minutes a person will fall sick