Amanda exercised for 10 minutes every day in the first week, 20 minutes in the second week, 30 minutes in the third week, and 40 minutes in the fourth week. Billy exercised for 5 minutes every day in the first week, 10 minutes in the second week, 20 minutes in the third week, and 40 minutes in the fourth week. Which statement best describes the methods used by Amanda and Billy to increase the time they spent exercising? (1 point) a Amanda's method is linear because the number of minutes increased by an equal number every week. b Billy's method is linear because the number of minutes increased by an equal factor every week. c Both Billy's and Amanda's methods are exponential because the number of minutes increased by an equal factor every week. d Both Billy's and Amanda's methods are exponential because the number of minutes increased by an equal number every week.
Answers
Answer:
The correct answer will be option (a).
Step-by-step explanation:
Amanda's method is linear because she is increasing her time period arithmetically and Billy's method is exponential because he is increasing his time period geometrically.
Given : Amanda exercised for 10 minutes every day in the first week, 20 minutes in the second week, 30 minutes in the third week, and 40 minutes in the fourth week.
Billy exercised for 5 minutes every day in the first week, 10 minutes in the second week, 20 minutes in the third week, and 40 minutes in the fourth week.
To Find : Which statement best describes the methods used by Amanda and Billy to increase the time they spent exercising?
a Amanda's method is linear because the number of minutes increased by an equal number every week.
b Billy's method is linear because the number of minutes increased by an equal factor every week.
c Both Billy's and Amanda's methods are exponential because the number of minutes increased by an equal factor every week.
d Both Billy's and Amanda's methods are exponential because the number of minutes increased by an equal number every week.
Solution :
Amanda exercised for 10 minutes every day in the first week, 20 minutes in the second week, 30 minutes in the third week, and 40 minutes in the fourth week.
20 - 10 = 30 - 20 = 40 - 30 = 10
Increase in time for a day is 10 minutes every week
Hence this is a linear relationship
Billy exercised for 5 minutes every day in the first week, 10 minutes in the second week, 20 minutes in the third week, and 40 minutes in the fourth week.
10/5 = 20/10 = 40/20 = 2
Hence Every week time is getting doubled
so Exponential
from the given options: correct is
a Amanda's method is linear because the number of minutes increased by an equal number every week.
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