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Janelle invests in a piece of art that cost 600 British Pounds. A study found that art appreciates in value at a rate of 3.97% per year. Assuming this pattern continues, how much, in British Pounds, will Janelle's piece of art be valued at after 10 years? Round your answer to the hundredths place.

Sagot :

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(10)=600(1.0397)^{10}=885.58793\approx885.59[/tex]

Hence, It will be worth about £885.59 after 10 years.

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