Question

the table shows the numbers y (in thousands) of people in a city who regularly use sharable electric scooters x weeks after the scooters are introduced.
write a function that models the data. round each coefficient to the nearest thousandth.
use the model to predict the number of users after 32 weeks. round the number of users to the nearest hundred.

Explanation:

Step1: Enter data into calculator

Using a graphing calculator (or statistical software), enter the \(x\) - values (time in weeks) and \(y\) - values (number of users in thousands) into the list editor.

Step2: Perform exponential regression

On the calculator, select the exponential regression function (\(y = ab^{x}\)). After running the regression, we get \(a\approx1.179\) and \(b\approx1.123\). So the function is \(y = 1.179(1.123)^{x}\).

Step3: Predict for \(x = 32\)

Substitute \(x = 32\) into the function \(y = 1.179(1.123)^{32}\).
First, calculate \(1.123^{32}\approx33.97\).
Then, \(y=1.179\times33.97\approx40.15\) (in thousands).

Answer:

The function is \(y = 1.179(1.123)^{x}\). The number of users after 32 weeks is approximately \(40200\) (since \(y\approx40.15\) thousand and \(40.15\times1000 = 40150\approx40200\) when rounded to the nearest hundred).