Two high school students are hired to rake leaves. they will work a couple hours each afternoon until the job is completed. they can choose one of the two payment plans. plan a pays $11.50 per afternoon, while plan b pays 2 cents for one day of work, 4 cents total for two days of work, 8 cents for three days of work, 16 cents total for four days, and so on. each student chooses a different plan. on which day would their total pay be approximately the same?

x = 14 days

Step-by-step explanation:

To answer the question, find a function that represents the payment mode of plan A and an equation that represents the mode of payment of plan B.

For Plan B the payment is constant every afternoon, $ 11.5 (or 1150 cents) so the equation to represent this form of payment is as follows:

A = 1150x (with units in cents)

This equation represents the line of a line of slope 1150, which passes through point (0,0). Where x is the number of days {1, 2, 3 ....}

In form of payment B, the amount of payment is doubled each day. And the first payment is 2 cents. Therefore this model is represented by an exponential base 2 equation of the form:

Where x represents the number of days, which is always greater than 0 {1, 2, 3, 4 ...}

To know in which day the salary will be approximately the same we equate both equations and we clear x.

A = B

It is a somewhat difficult equation to solve, so I recommend iterating to get a value where the function approaches 0 (when this difference is zero it means that the A and B salaries are the same).

Suppose

x = 13 days

cents

It is not equal to 0.

Let's try with x = 15

cents

Then the value that makes the function zero is between x = 13 and x = 15

Let's try with x = 14

cents = 2.84 $ difference. X = 14 is the whole number where functions A and B are closer together (the salary is approximately the same). Therefore the answer is

x = 14 days

for the points! : )

the answer would be 150 books

step-by-step explanation:

if you divide 300 by 2 you will get 150