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

Answer:

The correct option is 3.

Step-by-step 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

$V(t)=450\cdot(2)^{\frac{t}{5}}$

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.

$V(10)=450\cdot(2)^{\frac{10}{5}}$

$V(10)=450\cdot(2)^{2}$

$V(10)=450\cdot 4$

$V(10)=1800$

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