4x Bella's truck was worth 40,500 when she purchased it.The truck is depreciating at a rate of of 3.25% each year. 3.25% Select the value from the drop-down menu that correctly completes the statement. To the nearest dollar the truck will be worth 27,244 after square years.

## Step 1<br />The problem involves the concept of depreciation, which is a common topic in financial mathematics. The truck's value decreases each year by a certain percentage, which is 3.25% in this case. The question asks us to find out how many years it will take for the truck to depreciate to a value of $27,244.<br /><br />## Step 2<br />We can use the formula for exponential decay to solve this problem. The formula is:<br /><br />### \(A = P(1 - r)^t\)<br /><br />where:<br />- \(A\) is the amount of money accumulated after \(n\) years, including interest.<br />- \(P\) is the principal amount (the initial amount of money).<br />- \(r\) is the annual depreciation rate (in decimal).<br />- \(t\) is the time the money is invested for, in years.<br /><br />## Step 3<br />In this problem, we know that \(A = \$27,244\), \(P = \$40,500\), and \(r = 3.25\% = 0.0325\). We need to solve for \(t\).<br /><br />## Step 4<br />We can rearrange the formula to solve for \(t\):<br /><br />### \(t = \frac{\log(A/P)}{\log(1 - r)}\)<br /><br />## Step 5<br />Substitute the given values into the formula:<br /><br />### \(t = \frac{\log(27,244/40,500)}{\log(1 - 0.0325)}\)<br /><br />## Step 6<br />Calculate the value of \(t\).