117k views
4 votes
A population of beetles are growing accordingto a linear growth model. The initial population (week 0) isPo = 5, and the population after 7 weeks is P = 82.Find an explicit formula for the beetle population after n weeks..Pn-After how many weeks will the beetle population reach 258?weeks

User Aremmell
by
7.3k points

1 Answer

5 votes

Answer:

P(n) = 5 + 11n

n = 23 weeks

Step-by-step explanation:

The equation for the population as a linear growth model has the form

P = P0 + an

Where P0 is the initial population, n is the number of weeks and a is the rate of increase per week. We know that P0 = 5, so

P = 5 + an

Additionally, when n = 7 the value of P = 82, so we can use this to find the value of a as follows

82 = 5 + a(7)

82 = 5 + 7a

82 - 5 = 5 + 7a - 5

77 = 7a

77/7 = 7a/7

11 = a

Therefore, the equation for the population after n weeks is

P(n) = 5 + 11n

Finally, to know the number of weeks to reach a population of 258, we need to replace P by 258 and solve for n, so

258 = 5 + 11n

258 - 5 = 5 + 11n - 5

253 = 11n

253/11 = 11n/11

23 = n

So, after 23 weeks the population will be 258.

User Snez
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories