Considering the given function in the problem, it is found that:
a. 9.6 offspring survive to maturity when there are 12 female rabbits in the population.
b. At least 18 female rabbits are required for there to be 13 offspring.
The function gives the relationship between the number of adult female rabbits F and the number of offspring R as follows:
[tex]R = 3 + \frac{350F}{F + 625}[/tex]
When there are 12 female rabbits, we have that F = 12, hence:
[tex]R = 3 + \frac{350 \times 12}{12 + 625} = 9.6[/tex]
9.6 offspring survive to maturity when there are 12 female rabbits in the population.
For at least 13 offspring, we have that the number of rabbits needed is given as follows:
[tex]R \geq 13[/tex]
[tex]3 + \frac{350F}{F + 625} \geq 13[/tex]
[tex]\frac{350F}{F + 625} \geq 10[/tex]
[tex]350F \geq 10F + 6250[/tex]
[tex]F \geq \frac{6250}{340}[/tex]
[tex]F \geq 18[/tex]
At least 18 female rabbits are required for there to be 13 offspring.
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