Question

Marcus is doing a science fair experiment in which he measures the rate at which Bacteria multiply.Every 15 seconds , the bacteria double in numbers . If there are 10 now , how many will there be in 2 minutes?

Answer 1

Answer: 495 bacteria in 2 minutes.

Step-by-step explanation:

We would apply the formula,

y = ab^t

Where

a represents the initial amount of bacteria.

t represents the doubling time.

From the information given

a = 10

t = 15 seconds

Since after 15 seconds, the amount of bacteria multiplies by 2, then

y = 2 × 10 = 20

Therefore

20 = 10 × b^15

Dividing through by 10, it becomes

2 = b^15

Raising both sides of the equation by 1/15, it becomes

2^(1/15) = b^15/15

b = 1.047

The equation becomes

y = 10(1.047)^t

For t = 2 minutes(2 × 60 = 120 seconds), then

y = 10(1.047)^120

y = 495 bacteria