Question

The number of hours, t, that bacteria spread 10-fold can be modeled by the equation B(t) - Bo(10)21. There are 15 bacteria present initially and a biologist wishes to find out how many hours will elapse until there are 1,845 bacteria present. What is the exact value for the number of hours elapsed, t, in the equation 1,845= 15(10)2¹? (7 points)

Answer 1

B

Explanation:

In order to find the value of t in the given equation, we need to solve for t by isolating it on one side of the equation. We can do this by dividing both sides of the equation by 15 and then taking the logarithm of both sides with base 10. This gives us the equation:

t = log10(1,845/15)

We can now calculate the value of t by plugging in the given values and evaluating the logarithm:

t = log10(1,845/15) = log10(123.67) = 2.09

Therefore, the exact value for the number of hours elapsed, t, in the equation 1,845 = 15(10)2¹ is 2.09 hours.