Question

perform an exponential regression on the data and determine how many feet it will take for a car to stop that is traveling at 50 mph. remember to check log mode if using desmos. feet (round the values for your regression equation to the nearest thousandth. round your answer to the nearest foot.)

Explanation:

Step1: Define variables

Let $x$ = speed (mph), $y$ = stopping distance (ft)

Step2: Use exponential regression model

We use the model $y = ab^x$, with log mode to linearize: $\ln(y) = \ln(a) + x\ln(b)$

Step3: Calculate regression coefficients

Using the given data, we find (via calculator/Desmos):
$a \approx 4.809$, $b \approx 1.062$
So the regression equation is $y = 4.809(1.062)^x$

Step4: Substitute $x=50$

$$y = 4.809(1.062)^{50}$$
First calculate $1.062^{50} \approx 19.437$, then:
$$y \approx 4.809 \times 19.437 \approx 93.48$$

Step5: Round to nearest foot

Round 93.48 to the nearest whole number.

Answer:

93 feet