Question

between 12:00 pm and 1:00 pm, cars arrive at a local banks drive - thru at the rate of 4 cars per hour (0.07 car per minute). the formula below from probability can be used to determine the probability that a car will arrive within t minutes of 12:00 pm. use this information to answer the questions in parts (a)-(c).
f(t)=1 - e^{-0.07t}
(a) graph f using a graphing utility. which graph is the graph of f(t)?

Explanation:

Step1: Analyze the function form

The function $F(t)=1 - e^{-0.07t}$ is an exponential - type function. When $t = 0$, $F(0)=1 - e^{0}=1 - 1=0$.

Step2: Consider the behavior as $t$ increases

As $t
ightarrow+\infty$, $e^{-0.07t}
ightarrow0$, so $F(t)
ightarrow1$. The function is non - negative and increasing for $t\geq0$.

Step3: Evaluate the options

Option A has a negative $y$ - intercept which is incorrect since $F(0) = 0$. Option B is a decreasing function which is wrong as $F(t)$ is increasing. Option C has $y(0)=0$ and is an increasing function approaching $y = 1$ as $t$ increases.

Answer:

C