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.

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

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