A population of beetles are growing according to a linear growth model. The initial population (week 0) is P0=6, and the population after 8 weeks is P8=86 Find an explicit formula for the beetle population after n weeks.

After how many weeks will the beetle population reach 236?

The number of weeks it will take for the  beetle population to reach 236 is 28.75.

Step-by-step explanation:

If a quantity starts at size P₀ and grows by d every time period, then the

quantity after n time periods can be determined using explicit form:

Here,

d = the common difference, i.e. the amount  that the population changes each time n is increased by 1.

In this case it is provided that the original population of beetle was:

P₀ = 6; (week 0)

And the population after 8 weeks was,

P₈ = 86

Compute the value of d as follows:

Thus, the explicit formula for the beetle population after n weeks is:

Compute the number of weeks it will take for the  beetle population to reach 236 as follows:

Thus, the number of weeks it will take for the  beetle population to reach 236 is 28.75.