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The value of a truck decreases exponentially since its purchase. The two points on the graph shows the truck's initial value and its
value a decade afterward.
50
(0,40,000)
40
30
value in thousands of dollars
20
01.24.000)
10
05
1
decades since purchase
Express the car's value, in dollars, as a function of time d, in decades, since purchase.

Answer :

The exponential function that gives the car's value, in dollars, as a function of time d, in decades, since purchase is given as follows:

[tex]V(d) = 40000(0.6)^d[/tex]

What is an exponential function?

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

  • A(0) is the initial value.
  • r is the decay rate, as a decimal.

In this problem:

  • Point (0,40000) means that the car was worth $40,000 initially, hence A(0) = 40000.
  • Point (1,24000) means that in a decade, the car value was worth 24/40 = 0.6 of the initial value, hence 1 - r = 0.6.

Hence, the exponential function is given by:

[tex]V(d) = 40000(0.6)^d[/tex]

More can be learned about exponential functions at https://brainly.com/question/25537936

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