Question

Every hour, the mass of bacteria in a sample multiplies by 3.

If the sample contains 7 mg of bacteria to start with, how many milligrams (mg) will it contain after
a) 4 hours?
b) 5 hours?

Answer 1

After 4 hours, the mass of bacteria will be 567 mg, and after 5 hours, it will increase to 1701 mg, calculating by multiplying the initial mass by three to the power of the number of hours.

Step-by-step explanation:

The student's question deals with exponential growth, specifically in the context of a bacteria population that multiplies by a factor every hour. To find the mass of bacteria after a certain number of hours, we use the formula final mass = initial mass × growth ratenumber of hours.

For part (a):

After 4 hours, the mass of bacteria will be:

7 mg × 34 = 7 mg × 81 = 567 mg

For part (b):

After 5 hours, the mass of bacteria will be:

7 mg × 35 = 7 mg × 243 = 1701 mg