Question 1150408
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The phrase "its rate of appreciation at any time is proportional to its value at that time" means this is exponential growth.<br>
The basic formula for exponential growth is<br>
{{{y = a(b^x)}}}<br>
a is the initial value and b is the (annual) growth factor.<br>
The current value is 35,000.<br>
The growth factor over 10 years is {{{35000/25000 = 7/5 = 1.4}}}; the annual growth factor is {{{(1.4)^(1/10)}}}.<br>
The number of years it will take the value to increase to 50,000 is found by solving the equation<br>
{{{35000(1.4)^((1/10)^x) = 35000(1.4)^(x/10) = 50000}}}<br>
Graphing the expressions on both sides of the equation on a graphing calculator shows the solution to be 10.6 years.<br>