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.
Answer:
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
