Transforming Exponential Expressions
Interactive practice questions
Consider the function $f\left(t\right)=2\left(\frac{3}{8}\right)^t$f(t)=2(38)t, where $t$t represents time.
What is the initial value of the function?
Express the function in the form $f\left(t\right)=2\left(1-r\right)^t$f(t)=2(1−r)t, where $r$r is a decimal.
Does the function represent growth or decay of an amount over time?
growth
decay
What is the rate of decay per time period? Give the rate as a percentage.
Consider the function $f\left(t\right)=\frac{8}{7}\left(\frac{3}{8}\right)^t$f(t)=87(38)t, where $t$t represents time.
Consider the function $f\left(t\right)=\frac{5}{6}\left(2\right)^t$f(t)=56(2)t, where $t$t represents time.
Starting at $k$k grams, the amount of radium-226 in a sample after $\frac{t}{1602}$t1602 years is given by $A=k\left(\frac{1}{2}\right)^{\frac{t}{1602}}$A=k(12)t1602.