Question

A store’s sales (in thousands of dollars) grow according to the recursive rule Pn=Pn-1 + 15, with initial population P0=40.

Calculate P1 ________
Calculate P2 _______
Find the explicit formula for the line: Pn=_______+________n
Predict the store’s sales in 10 years. _______

Answer 1

The store's sales grow according to the recursive rule Pn=Pn-1 + 15.

a) P1 is 55,

b) P2 is 70,

c) the explicit formula is Pn = 40 + 15n.

d) The predicted sales in 10 years is 190.

Step-by-step explanation:

a) To calculate P1, we substitute the value of n-1 in the recursive rule.

Therefore, P1 = P0 + 15

= 40 + 15

= 55.

b) To calculate P2, we substitute the value of n-1 in the recursive rule.

Therefore, P2 = P1 + 15

= 55 + 15

= 70.

c) The explicit formula for the line is Pn = P0 + 15n.

In this case, Pn = 40 + 15n.

d) To predict the store's sales in 10 years, we substitute the value of n in the explicit formula.

Therefore, P10 = 40 + 15(10)

= 40 +150

= 190.