Cecelia studied for the SAT for 20 minutes every day in the first week, 30 minutes in the second week, 40 minutes in the third week, and 50 minutes in the fourth week.Christopher studied for the SAT 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 Cecelia and Christopher to increase the time they spent studying? A. Cecelia's method is exponential because the number of minutes increased by an equal number every week.B. Christopher's method is exponential because the number of minutes increased by an equal factor every week. C. Both Christopher's and Cecelia's methods are linear because the number of minutes increased by an equal factor every week.D. Both Christopher's and Cecelia's methods are linear because the number of minutes increased by an equal number every week.
Accepted Solution
A:
Answer:Option B.Step-by-step explanation:Cecelia studied for the SAT for 20 minutes every day in the first week, 30 minutes in the 2nd week, 40 minutes in 3rd week and 50 minutes in 5th week.So the sequence formed is 20, 30, 40, 50This sequence has a common difference of [tex]T_{2}-T_{1}=30-20=10[/tex][tex]T_{3}-T_{2}=40-30=10[/tex]Therefore, this sequence is an arithmetic sequence or linear sequence.Christopher studied for the SAT for 5 minutes every day in the first week, 10 minutes in 2nd week, 20 minutes in 3rd, 40 minutes in 4th week.Sequence formed is 5, 10, 20, 40.It's an exponential or geometric sequence which has a common ratio r = [tex]\frac{T_{2} }{T_{1}}=\frac{T_{3} }{T_{2}}[/tex] = [tex]\frac{20}{10}=2[/tex]Therefore, Option B will be the answer.