SAT Mathematics Practice Test 4

According to the analyst’s estimate, the value V, in dollars, of the stock will decrease by 28% each week for t weeks, where t = 1, 2, or 3, with its value being given by the formula $\mathit{V}=360{\left(\mathit{r}\right)}^{\mathit{t}}.$ This equation is an example of exponential decay. A stock losing 28% of its value each week is the same as the stock’s value decreasing to 72% of its value from the previous week, since $\mathit{V}-\left(.28\right)\mathit{V}=\left(.72\right)\mathit{V}.$ Using this information, after 1 week the value, in dollars, of the stock will be $\mathit{V}=360\left(.72\right);$ after 2 weeks the value of the stock will be $\mathit{V}=360\left(.72\right)\left(.72\right)=360{\left(.72\right)}^2;$ and after 3 weeks 1 the value of the stock will be $\mathit{V}=360\left(.72\right)(.72\left(.72\right)=360{\left(.72\right)}^3$.For all of the values of t in question, namely $\mathit{t}=1,2,$ and $3$, the equation $\mathit{V}=360{\left(.72\right)}^{\mathit{t}}$ is true. Therefore, the analyst should use .72 as the value of r.