(Solved): The formula for exponential growth is \( y=a(1+r)^{t} \), where \( a \) is the initial amount, \( r ...

The formula for exponential growth is \( y=a(1+r)^{t} \), where \( a \) is the initial amount, \( r \) is the rate of growth, and \( t \) is the number of intervals. Use the formula to determine the answer to the following problem. In 2010 , there were 2,458 students who successfully completed Algebra II. If the success rate for completing Algebra II increases by \( 1.5 \% \) a year, how many students successfully completed Algebra II in 2017 ? \( \begin{array}{ll}\text { a } & 2,476 \\ \text { b } & 2,728 \\ \text { c } & 2,300 \\ \text { d } & 2,707\end{array} \) The formula for exponential decay is \( y=a(1-r)^{t} \), where \( a \) is the initial amount \( r \) is the rate of decay and \( t \) is the number of intervals. Use the formula to determine the answer to the following problem. On Monday, your teacher gives you a list of twenty square roots to be memorized. You memorize all of them Monday night and do not look at the list again. If you forget \( 3 \% \) of the list each day, how many square roots will you remember three days later? What is the explicit definition for the sequence defined by the recursive equation shown below? \[ \left\{\begin{array}{l} a_{1}=15 \\ a_{n}=\left(\frac{1}{5}\right) a_{n-1} \end{array}\right. \] a \( \quad a_{n}=\left(\frac{1}{5}\right) a_{n-1} \) ? \( a_{n}=15\left(\frac{1}{5}\right)^{n-1} \) ? \( \quad a_{n}=15 a_{n-1} \) d \( a_{n}=\left(\frac{1}{5}\right)(15)^{n-1} \)