Question

Jackson is starting an exercise program. The first day he will spend 30 min. on a treadmill. He will increase his time on the treadmill by 2 min. each day. Write an equation T(D) the time in min. on the treadmill on day d)

Find t(6)

Answer 1

The equation for the time Jackson spends on the treadmill on day d is T(d) = 2d + 30. To calculate the time on day 6, we plug in the value of 6 into the equation, yielding T(6) = 42 minutes.

Step-by-step explanation:

Jackson will spend 30 minutes on the treadmill on his first day and he will increase his time by 2 minutes each day thereafter. To write an equation T(d) for the time in minutes on the treadmill on day d, we first recognize this as a linear relationship with a starting value (y-intercept) of 30 minutes and a slope (rate of increase) of 2 minutes per day. Hence, the equation will be of the form:

T(d) = 2d + 30

This equation resembles the format of a linear equation y = mx + b, where m is the slope and b is the y-intercept. Here, d is the number of days and T(d) is the total time on the treadmill. Now, let's find t(6), which corresponds to the time Jackson will spend on the treadmill on day 6:

T(6) = 2(6) + 30
= 12 + 30
= 42 minutes

So, on day 6, Jackson will spend 42 minutes on the treadmill.