Craig earns extra money as a lifeguard. He earns $36 for 4 hours and $63 for 7 hours. Determine the constant of proportionality.
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Answer:
The population when t = 3 is 10.
Step-by-step explanation:
Suppose a certain population satisfies the logistic equation given by
with P(0)=1. We need to find the population when t=3.
Using variable separable method we get
Integrate both sides.
.... (1)
Using partial fraction
Using these values the equation (1) can be written as
On simplification we get
We have P(0)=1
Substitute t=0 and P=1 in above equation.
The required equation is
Multiply both sides by 10.
Reciprocal it
The population when t = 3 is
Using calculator,
Therefore, the population when t = 3 is 10.