Chapter 5.1, Problem 21E

(a)

To determine

To calculate: The value of $a$ for which $a>1$ and express the function $y=3{\left(\frac{2}{5}\right)}^x$ in the form of $y=3\left(a^{-x}\right)$.

(b)

To determine

Whether the functions $y=3{\left(\frac{2}{5}\right)}^x$ and $y=3{\left(2.5\right)}^{-x}$ have exponential growth or exponential decay. Also give the explanation.

(c)

To determine

To graph: The functions $y=3{\left(\frac{2}{5}\right)}^x$ and $y=3{\left(2.5\right)}^{-x}$ to check that the functions have exponential decay.