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Answer:
a.
b.
c.13.3 months
Step-by-step explanation:
a.-Given the first term at is 6 and the second term at
is 32.
-Let's take rabbit population as a function of time to be
where y is the population at time x and a the initial population at
#We substitute our values to calculate the value of the constant b:
#Replace b in the population function:
Hence, the regression for the rabbit population as a function of time x is
b. The exponential function in terms of base is usually expressed as:
Where:
-is the initial population at
-is the population at time t.
is the exponential growth constant.
the exponent
Our function in terms of base exponent is rewritten as:
#Substitute with actual figures to solve for t:
Hence, the regression equation in terms of base e is
c. We substitute y with any number higher than 10,000 to estimate the time for the rabbits to exceed 10,000.
-We know that
Therefore we calculate t as(take y=10001):
Hence, it takes approximately 13.3 months for the population to exceed 10000