HSF.IF.C.8.b Tutor Intake — Interpreting Exponential Function Parameters

Which statement correctly describes $y = 3000(0.88)^t$?

The function $f(t) = 500(1.06)^t$ has a growth factor of $1.06$.

What is the percent growth rate per unit of $t$?
Enter as a whole number (e.g., enter $6$ for $6\%$).

For $y = A \cdot b^t$, which condition on $b$ guarantees exponential decay?

The function $V(t) = 8000(0.75)^t$ models the value of a machine in dollars,
$t$ years after purchase.

What is the percent rate of decay per year? Enter as a whole number
(e.g., enter $15$ for $15\%$).

A radioactive substance has a half-life of 5 years. Its amount is modeled by
$A(t) = 200\left(\tfrac{1}{2}\right)^{t/5}$.

After rewriting in the form $A(t) = 200 \cdot b^t$, which value is closest
to the base $b$?

A savings account earns $1\%$ interest per month, modeled by $y = P(1.01)^{12t}$
where $t$ is measured in years.

Which expression shows the equivalent annual growth factor?

The function $y = P(1.01)^{12t}$ can be rewritten as $y = P(1.01^{12})^t$.

Using a calculator, $1.01^{12} \approx 1.1268$.

What is the approximate annual percent growth rate? Enter as a number
rounded to two decimal places (e.g., enter $12.68$ for $12.68\%$).

Determine whether $f(t) = 400 \cdot 4^{-t/3}$ represents growth or decay,
and identify the approximate percent rate per unit of $t$.