Question

A population of beetles are growing according to a linear growth model. The initial population (week 0) is p0=6 and the population after 7 weeks is p7=83 find an explicit formula for the beetle population after n weeks.

Answer 1

P(n)= p0 + 11(n)

Where p0= population of week 0

P(n) = population of n weeks

n= number of weeks

Explanation:

Population of beetles in Week 0= 6

Population of beetles in Week 7= 83

From week 0 to week 7 there are 8 weeks.

But subtracting population of week 0 from population of week 7 gives

= 83-6

= 77

After the subtraction, we have 7 weeks remaining.

Dividing the remaining population by the number of weeks remaining

=77/7

= 11

For n number of weeks, population p of beetles

P(n)= p0 + 11(n)

Where p0= population of week 0

P(n) = population of n weeks

n= number of weeks