(a)

The function is .

Find number of insects at days.

Substitute .

.

Number of insects at days is .

(b)

The size of poulation after hours is .

Where is the exponential growth rate.

The equation is .

Compare the equation with .

.

Therefore, the growth rate is per day.

(c)

Find the population after days.

Substitute in .

Number of insects after days is insects.

(d)

Find the number of days taken to reach the population of insects.

Substitute in the equation .

Take natural logarithm on each side.

The population of insects is insects after days.

(e)

The equation is .

Find the time when the population of the insects is double.

Therefore, .

Substitute in .

Take natural logarithm on each side.

The population of insects is double insects after days.

(a) Number of insects at days is insects.

(b) The growth rate is per day.

(c) Number of insects after days is insects.

(d) The population of insects is insects after days.

(e) The population of insects is double insects after days.

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