Question

Please help, in desperate need!

Having wrapped up your last project, you begin to pack up when you see a text from Casey. They
noticed that you were in the office and were hoping you could do one final check on one of their slow-
growing bacteria that they are working on. Wanting to be helpful, you check on the results and see that
the computer has generated a population model P (t) = 224,841e0.15t where t is measured in days.
Casey would like to know how many days will it take for the population to reach one million, assuming
this model holds?
Round your answer to the nearest hundredth of a day (i.e. 2 decimal places).
The population will reach one million in Number
days.

Answer 1

9.95 days

Explanation:

Using the population model P(t) = 224841e^(.015t), you want to know how many days it will take for the population to reach 1 million.

Solution

Substituting 1,000,000 for P(t), we can solve for t.

1,000,000 = 224,841·e^(0.15t)

1,000,000/224,841 = e^(0.15t) . . . . divide by 224841

ln(1000000/224841) = 0.15t . . . . . . take natural logs

t = ln(1000000/224841)/0.15 ≈ 9.95 . . . . . divide by coefficient of t

The population will reach 1 million in 9.95 days.

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