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| PAGE: 330 | SET: Exercises | PROBLEM: 1 |
(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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