Answer:
It will be worth about £885.59.
Step-by-step explanation:
The art piece originally costs £600.
And it appreciates at a rate of 3.97% each year.
And we want to find the value of the art after 10 years.
We can write an exponential function to model the situation. The standard exponential function is given by:
[tex]f(t)=a(r)^t[/tex]
Where t is the time in years.
Since it appreciates at a rate of 3.97% each year, the value after each year will be (100% + 3.97%) or 103.97%.
103.97% = 1.0397. So, r = 1.0397:
[tex]f(t)=a(1.0397)^t[/tex]
Our a is the initial value. Therefore:
[tex]f(t)=600(1.0397)^t[/tex]
Then the value of the piece of art after 10 years is:
[tex]f(t)=600(1.0397)^{10}=885.5879...\approx \pounds 885.59[/tex]
It will be worth about £885.59 after 10 years.
