James wants to compete in the international speed texting competition next year where participants compete on text speed and accuracy. James's current text speed is 2 characters per second. James has found that his texting speed is increasing at a rate of ½ a character per second for each month that he practices.

Complete question :

James wants to compete in the international speed texting competition next year where participants compete on text speed and accuracy. James’s current text speed is 2 characters per second. James has found that his texting speed increases at a rate of 1⁄2 a character per second for each month that he practices.

1. a. What is James’s new texting speed if he practices for only 1 month?

b. What is James’s new texting speed if he practices for 2 months?

c. What is his new texting speed if he practices for 3 months?

d. Write an algebraic equation that gives James’s texting speed s for m months of

practice.

2 1/2 ; 3, 3 1/2 ; s = 2 + 1/2m

Step-by-step explanation:

Given that :

Speed = 2 characters per second

Rate of change = 1/2 character per second increase per month

New texting speed after 1 month :

Initial speed + (change per month * number of months)

2 + 1/2 * 1

= 2 1/2 or 2.5

After 2 months :

Initial speed + (change per month * number of months)

2 + (1/2 * 2)

2 + 1

= 3 characters per second :

After 3 months :

Initial speed + (change per month * number of months)

2 + 1/2 * 3

= 2 + 1.5

= 3.5

For the algebraic equation :

New texting speed, s

Number of months, m

Initial speed + (change per month * number of months)

s = 2 + 1/2 * m

s = 2 + 1/2m