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
can someone do this problem for me would be a big help.

Answer 1

The value of the painting after 10 years is $1,800

Explanation:

V(t) = 450 x 2 ^t/5

V(10) = 450 x 2^10/5

V(10) = 1,800

Answer 2

In order to find the answer for this problem, there are two ways to do that.
Analyze the problem. The paint costs $450 at present. This doubles after 5 years which makes it $900. Another 5 years, which is 10 years in total, it will be $1800.
Next, solve it using this equation:
450×2^t/5 where t is the number of years which is 10.
450×2^10/5
450×2^2
450 x 4 = $1800.
Still the answer is the same. So the answer would be the third option. Hope this answer helps.