Question 1204621: A population of beetles are growing according to a linear growth model. The population in the third week was𝑃3 = 18, and the population after 8 weeks is 𝑃8 = 38.
a. Find an explicit formula for the beetle population after n weeks.
b. After how many weeks will the beetle population reach 82?
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! A population of beetles are growing according to a linear growth model. The population in the third week was𝑃3 = 18, and the population after 8 weeks is 𝑃8 = 38.
a. Find an explicit formula for the beetle population after n weeks.
b. After how many weeks will the beetle population reach 82?
An arithmetic progression , the nth term is given by
Pn = a+(n-1)d
𝑃3 = 18, and the population after 8 weeks is 𝑃8 = 38.
18 =a+(3-1)d
18=a+2d--------------1
38= a+(8-1)d
38= a+7d--------------2
solve 1 &2 we get d=4 and a =10
Pn= 10+(n-1)4
Pn = 10+4n-4
Pn = 4n+6
After how many weeks will the beetle population reach 82?
82 = 4*n+6
76= 4n
19=n
After 19 weeks beetle population will reach 82
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