Question

Scott and Harry went cycling every day. They increased the number of minutes of cycling every week as described below: Scott: Cycled for 10 minutes every day in the first week, 15 minutes in the second week, 20 minutes in the third week, and 25 minutes in the fourth week. Harry: Cycled for 10 minutes every day in the first week, 20 minutes in the second week, 40 minutes in the third week, and 80 minutes in the fourth week. Which statement best describes the methods used by Scott and Harry to increase the time they spent cycling? Scott's method is linear because the number of minutes increased by an equal number every week. Harry's method is linear because the number of minutes increased by an equal factor every week. Both Harry's and Scott's method is exponential because the number of minutes increased by an equal factor every week. Both Harry's and Scott's method is exponential because the number of minutes increased by an equal number every week.

Answer 1

scott's method is linear because the number of minutes increased by an equal number every week. Because he increased each week by 5 minutes while Harry increased by a different amount of time each week

Answer 2

Scott's method is linear because the number of minutes increased by an equal number each week.

Arithmetic progressions use the linear method.

The graph proves it, by obtaining a straight line.

Explanation:

Scott used an arithmetic progression, with a ratio of 5, that is adding 5 to the value of each previous week.

Let us call the time in minutes of each week, so the arithmetic progression is of the following linear form:

S1 = k0 = 10

S2 = k1 + 5 = 10 + 5 = 15

S3 = k2 + 5 = 15 + 5 = 20

S4 = k3 + 5 = 20 + 5 = 25

See attached chart.

Harry used a geometric progression, with a ratio of 2, that is multiplying by 2 the value of each week.

Let us call time in minutes of each week, so the geometric progression is of the following exponential form:

S1 = k0 = 10

S2 = k1 x 2 = 10 x 2 = 20

S3 = k2 x 2 = 20 x 2 = 40

S4 = k3 x 2 = 40 x 2 = 80

See attached chart.

Let's analyze the four options given:

Scott's method is linear because the number of minutes increased by an equal number each week.

True: The graph proves it, by obtaining a straight line.

Also, Arithmetic progressions use the linear method.

Harry's method is linear because the number of minutes increased by an equal factor each week.

False: The graph shows that it is not linear, a straight line is not obtained.

Both Harry and Scott's method are exponential because the number of minutes increases by an equal factor each week.

False: Scott's method is linear.

Both Harry and Scott's method are exponential because the number of minutes increases by an equal number each week.

False: Scott's method is linear.