Sterile fruit flies are used in an experiment where the proportion that survives at least t days is given by e^−0.15t. if the experiment begins with 400 fruit flies, and flies are added at the rate of 6 per hour, how many flies are present 15 days after the start of the experiment? (round your answer to the nearest integer.)

901 flies

Step-by-step explanation:

Let the total population of flies is P,

While and represent the number of flies that survived and that are initially respectively.

Here,

Differentiating w. r. t. t ( time ),

Now, if 6 flies are added per hour,

Then the number of flies added per day = 24 × 6 = 144 ( ∵ 1 day = 24 hours),

So,

When P = =

∵ if t = 0, P = 400,

i.e. 901 flies would present.