average running speed of the train

Question

If the average running speed of an amateur athlete​ (in miles per​ hour) after training for t days is given by

S(t)=0.37lnt+11.6​, then answer the following. ROUND YOUR FINAL ANSWERS TO 2 DECIMAL

PLACES.

​A) Find the average running speed of amateur athletes that train for

106 days.      enter your response here miles per hour

​B) How many days of training would yield

an average speed of

13.9 miles per​ hour?       

enter your response here

days

Answer 1

a) Plug in 106 for the "t" variable which represents the time in days, then solve for S(t).

S(t)=0.37ln(106)+11.6

This gives us S(t)≈13.33 mph

b) Now, we plug in the 13.9 for S(t) as that represents our speed in mph, and then solve for t.

13.9=0.37ln(t)+11.6

t≈500.80 days

Hope this helps!