Question

Timothy has a plan to increase the number of sit-ups he does by the same percent each week. The table shows his goal for each week of the plan. Which expression gives the goal for the 26th week?

Answer 1

The expression for Timothy's goal for the 26th week is 120×(1.05)^26 .

Timothy's plan involves increasing the number of sit-ups each week by the same percent. The expression 120×(1.05)^26 represents the goal for the 26th week. Here's the breakdown:

The initial goal is 120 sit-ups, as indicated by the starting point.

The term (1.05)^26 accounts for the repeated weekly increase. Since Timothy is increasing by the same percent each week, the expression 1.05 represents a 5% increase (as a decimal) from the previous week. The exponent 26 corresponds to the number of weeks.

By multiplying the initial goal by the factor representing the consistent weekly increase for 26 weeks, the expression captures Timothy's cumulative goal for the 26th week in his plan to enhance his sit-up performance.