Question

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

Initial number of Bacteria = Ao = 100
Number of Bacteria which make the person ill = A = 45,000,000

Growth rate = r = 150% = 1.50 

The equation model for this situation is:

$A= A_{o}(1+r)^{t}$

Using the values in above equation, we can write:

$45000000=100(1+1.5)^{t} \\ \\ 450000=(2.5)^{t} \\ \\ log(450000)=log((2.5)^{t}) \\ \\ log(450000)=t*log(2.5) \\ \\ t= \frac{log(450000)}{log(2.5)} \\ \\ t=14.21$

This means, the person will fall sick after about 14 hours.

Answer 2

Answer:

14 hrs 12 minutes

Step-by-step explanation:

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

$P(t) = 100(1+1.5)^t$

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

i.e. $45,000,000=100(2.5)^t\\450000 =2.5^t$

Take log on both sides

$log 450000 = t log 2.5\\\\ 5.653 = 0.3979t\\t=14.21$

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