Question

(1 point) A store's sales (in thousands of dollars) grow according to the recursive rule PN = PN-1 + 15, where N represents the number of years after they began recording sales. Their sales in the first year are Po = 40. (a) Calculate P, and P2. P1 = P2 = (b) Find an explicit formula for Pn. Note: Webwork is case-sensitive here, so if you use the variable N in your answer you must keep it capitalized. Pn = (c) Use your formula to predict the store's sales in 10 years. 000 P10 = !!! 00 (d) When will the store's sales reach at least $120 thousand? If your answer is not a whole number, please round your answer up. N =

Answer 1

a. Given P_{​​​​​​0}​​​ = 40 and given equation is P_{​​​​​​N} = P_{​​​​N-1} + 15

So from the equation

P1 = P0 + 15 = 40 + 15 = 55

And P2 = P1 + 15 = 55 + 15 = 70

So P1 = 55 and P2 = 70

b. So we can consider the new formula for P_{​​​​​​N} by the fact that for every single increase of N the quantity P_{​​​​​​N} increases by 15 . So new formula is

P_{​​​​​​N} = 40 + 15N

c. P_{​​​​​​10} = 40 + 15×10 = 190

d. Here given P_{​​​​​​N = 120. We have to find the N.}

_{so, 40 +15N = 120}

_{=> 15N = 80}

_{​​​​​​ => N = 80/15 = 5.33 or 5}

_{therefore N = 5}