Question

The cost of producing transistors decreases by 20% every year. If it currently costs $440 to produce a billion transistors, how much will it cost to produce a billion transistors in 7 years? If necessary, round your answer to the nearest cent.

Answer 1

To estimate the cost of production after 7 years we use the exponential function given by:
y=ab^x
where:
y= cost after time x
a=initial cost
b=growth factor
thus plugging in the values in the expression we get:
y=440(0.80)^x
hence
when x=7, then:
y=440(0.8)^7
y=$92.275
y~$92.30

Answer 2

The applicable explicit formula for this scenario is:

C(n) = 440(1-0.2)^n, where C(n) = cost of production of billion transistors in year n.

In short,
C(n) = 440(0.8)^n

In seven years, n = 7 and therefore cost of production of billion transistors is,
C(n) = 440(0.8)^7 = $92.27