Question

A painting is purchased for $450. If the value of the painting doubles every 5 years, then its value is given by the function V(t) = 450 • 2t/5, where t is the number of years since it was purchased and V(t) is its value (in dollars) at that time. What is the value of the painting ten years after its purchase? $1,000 $1,400 $1,800 $2,000 i'm terrible at word problems, so if someone can give me step-by-step help, that would be amazing.

Answer 1

10 years divided by 5 years is 2 years(thats how many times u double) then double 450 once =900 then double it again=1800
so the answer would bw $1,800

Answer 2

The correct option is 3.

Explanation:

It is given that a painting is purchased for $450. If the value of the painting doubles every 5 years, then its value is given by the function

`V(t)=450\cdot(2)^{(t)/(5)}`

Where, t is the number of years since it was purchased and V(t) is its value (in dollars) at that time.

Substitute t=10 in the given function to find the value of the painting ten years after its purchase.

`V(10)=450\cdot(2)^{(10)/(5)}`

`V(10)=450\cdot(2)^(2)`

`V(10)=450\cdot 4`

`V(10)=1800`

The value of the painting ten years after its purchase is 1800, therefore the correct option is 3.