Question

The cost per hour of manufacturing widgets decreases exponentially according to the formula f(x) = (1/2)^x. The number of hours spent producing widgets at the factory in Bridgeton can be modeled by g(x) = 3x. Write a new function that represents the total cost that the Bridgeton factory spends on producing widgets.
Answer

t(x) = (3x)(1/2)^x

t(x) = (3/2)^x

t(x) = (3x) + (1/2)^x

t(x) = (1/2)^3x

Answer 1

well, think about it
people at the Bridgeton factory are going to work \(\bf 3x\) hours
and the factory management is spending over the same length of time \(\bf \pmatrix{\cfrac{1}{2}}^x\) amount of dollars to make the widgets

Answer 2

D

Answer 3

think about it this way
you go to work at IBM
IBM tells you that for every hour you work, they really spend $1,000 per chip made
so if you were to work say 5 hours, how much had they spent then?

Answer 4

5000

Answer 5

so you're really MULTIPLYING the hours spend in working making the chips, TIMES the cost to make the chips per hour
so is really

hours times cost

Answer 6

so, which of your choices gives you that?

Answer 7

A

Answer 8

yes, \(\bf t(x) = (3x)\pmatrix{\cfrac{1}{2}}^x\)