Question

The number of hours, t, that bacteria spread 10-fold can be modeled by the equation B(t) = B0(10)2t. There are 25 bacteria present initially and a biologist wishes to find out how many hours will elapse until there are 55,000 bacteria present. What is the exact value for the number of hours elapsed, t, in the equation 55,000 = 25(10)2t?

Answer 1

The number of hours elapsed, t, in the equation 55,000 = 25(10)2t is approximately 3.0445 hours.

Step-by-step explanation:

To find the number of hours, t, that will elapse until there are 55,000 bacteria present, we can use the equation B(t) = B0(10)2t and substitute the given values. We have 55,000 = 25(10)2t.

To solve for t, we need to isolate the variable. Divide both sides of the equation by 25 to get 2,200 = (10)2t.

Take the logarithm of both sides using base 10 to solve for t.

Log10(2,200) = Log10((10)2t). Log10(2,200) = 2t.

T = Log10(2,200) / Log10(10).

Using a calculator, we find that t is approximately equal to 3.0445 hours.