2700 candies
c(0) = 2700; c(n) = c(n-1) -7
c(n) = 2700 -7n
2693, 2686, 2679
Step-by-step explanation:
1. The number of candies in the machine is the product of the number of pounds of candy and the number of candies in a pound:
(15 lbs)(180 candies/lb) = 2700 candies
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2. c(0) = 2700; c(n) = c(n-1) -7 . . . . the new number of candies is 7 fewer than after the previous customer. After no customers, the number is the original 2700 candies.
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3. As the recursive formula tells us, the initial number of candies is 2700, and the number decreases at the rate of 7 per customer. The number remaining after n customers is ...
c(n) = 2700 -7n
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4. Evaluating the above formula for n=1, 2, 3, we get ...
c(1) = 2700 -7 = 2693 . . . . candies remaining after 1 customer
c(2) = 2700 -7·2 = 2686 . . . 2 customers
c(3) = 2700 -7·3 = 2679 . . . 3 customers
