Question

Mya is a performance athlete. She wants to use a function to represent the number of calories that she burns while training, where y

represents the total calories burned and a represents her training time in minutes. Mya estimates that the exponential function
y = 45.30.0548.2 is the best fit for the data. Given the following table, what is the actual number of calories that Mya burned when she
trained for 30 minutes? Round your answer to the nearest whole number.
I Need help plz

Answer 1

The actual number of calories that Mya burned when she

trained for 30 minutes is 240.

Explanation:

We have an exponential function that is the best fit for the number of calories Mya burns, in function of time (minutes).

The function is:

`y=45.3e^(0.0548x)`

Where y: calories burned, and x: training time.

Whenever we use regression models, we have a real value and a predicted value. The difference between them, the measure we want to minimize when we adjust with this typo of models, is called residual.

In the table is shown as one of the columns.

For example, for x=10 minutes, we have a real value of 30 and a predicted value of 78.36, so the residual becomes e=30-78.36=-48.36.

`e=y-\hat y=30-78.36=-48.36`

For x=30 minutes, we have only the residual, that has a value of 5.53. That means that the predicted value, which we can calculate, is 5.53 below the real value.

The predicted value for x=30 is:

`y(30)=45.3e^(0.0548*30)=45.3*5.18=234.47`

Using the equation for the residual e, we can calcualte the actual number of calories that Mya burned in 30 minutes:

`e=y-\hat y=y-234.47=5.53\\\\y=234.47+5.53\\\\y=240`