Question

Suppose that in her first year of school, Emma does 50 minutes of homework each week. The

second year of school, she does 60 minutes of homework each week, and the third year of
school, she spends 72 minutes on homework each week. Assuming that the number of minutes of
homework per week follows a consistent pattern of growth, about how many hours of homework
per week will Emma do in her 12th year of school?

Answer 1

Emma's homework time increases geometrically with a common ratio of 1.2. To find the 12th term of this geometric sequence, we use the formula for the nth term and then convert the result from minutes to hours.

Step-by-step explanation:

The question asks us to determine how many hours of homework Emma will do in her 12th year of school based on the pattern of growth in the minutes of homework she does each week over the first three years. To find this, we observe that her homework time is growing by a factor of 1.2 each year (60/50 = 1.2, 72/60 = 1.2). This appears to be geometric series where the first term, a, is 50 (minutes) and the common ratio, r, is 1.2. To find the homework time in the 12th year, we use the formula for the nth term of a geometric sequence:

Term(n) = a * r^(n-1)

For the 12th year: Term(12) = 50 * 1.2^(12-1) = 50 * 1.2^11

After calculating this value, we convert the minutes to hours by dividing by 60.

Therefore, Emma will spend approximately Term(12)/60 hours doing homework in her 12th year.