Question

In a lab, a colony of 100 bacteria is placed on a petri dish. The population triples every hour.

1. How would you estimate the population of bacteria in. Make the minutes into a decimal and tell me what to substitute. Be specific on what you would do

a. 90 minutes?

b. 30 minutes?

2. How would you estimate the number of hours it would take the population to grow to 1,000 bacteria. Be specific on what you would do.

Reply as answers 1a, 1b, 2.

Answer 1

1.a 519.615

1.b 173.21

2. It would take approximately 2.1 minutes

Explanation:

If the population triples every hour then after one hour the population must be:

population(0) = 100

population(1) = 100*3 = population(0)*3

After two hours:

population(2) = population(1)*3 = population(0)*3*3 = population(0)*3²

After three hours:

population(3) = population(2)*3 = population(0)*3²*3 = population(0)*3³

Therefore the equation that will model the growth of the population is:

population(n) = 100*3^n

1. a.

We first need to convert the time from minutes to hours, to do that we must divide by 60. We have:

time = 90/60 = 1.5

We then apply this value in the "n" from the equation above:

population(1.5) = 100*3^(1.5) = 519.615

1.b.

We have to follow the same steps as before:

time = 30/60 = 0.5

population(0.5) = 100*3^(0.5) = 173.21

2.

We now use the same equation as before, but we want to solve for n isntead of "population". We have:

1000 = 100*(3^n)

100*(3^n) = 1000

3^n = 1000/100

3^n = 10

ln(3^n) = ln(10)

n*ln(3) = ln(10)

n = ln(10)/ln(3) = 2.095

It would take approximately 2.1 minutes