You work in a lab and are growing a bacteria culture.

Question

Here is my question of Precalcus question,

You work in a lab and are growing a bacteria culture. Your assistant has estimated that the initial number of bacteria is 350. According to your manual, the number of bacteria in the culture can be modeled by the equation P=C*e^0.09t, where t represents the elapsed time in hours and C represents the initial population After 5 hours have elapsed, and you receive an email from your boss asking you to immediately run an expensive test on the culture; an important client is demanding immediate results. The test requires a population of at least 10,000 bacteria. You determine the test is not possible at the present time, and also the earliest time it would be possible. Write an explanation to your boss of why the test isn't possible now and how you determined when it would be possible. Include details of your computations, why you performed them, and what they tell you about the situation. Be clear and include all assumptions you are making, as well as any sources for what you are stating. (Your boss is very demanding and wants to know where all the numbers and equations come from, and if there is any possibility of error.)

Answer 1

P(t) = 350·e^0.09t

After t = 5 hours:

P(5) = 350·e^0.09·5 = 350·e^0.45 = ____? bacteria

Use your calculator to get the answer. Round to the nearest whole number (because you can't have part of a bacterium).

When you'll have 10,000:

10,000 = 350·e^0.09t

(1000/35) = e^0.09t

ln(1000/35) = 0.09t

ln(1000/35)/0.09 = t

Again, use your calculator to get the answer.