Question

Consider a population that grows according to the recursive rule P n = P n − 1 + 95 , with initial population P 0 = 60 . Then: P 1 = P 2 = Find an explicit formula for the population. Your formula should involve n (use lowercase n) P n = Use your explicit formula to find P 100 P 100 =

Answer 1

Answer:

Pn = P n-1 + 95

Po = 60

P1 = Po + 95

= 60 + 95

= 155

P2 = P1 + 95

= 155 + 95

= 250

Here we can say that, it is in the form of Arithmetic progression

i.e.,

Po = 60 , d = 95

So, Pn = Po + nd

i.e.,

Pn = 60 + n*95

Pn = 60 + 95n

P100 = 60 + 95*100

= 60 + 9500

P100 = 9560