Answer:
49 acres
Explanation:
Given that:
Initial coverage = 1200 at midnight
Spread rate = 5√t acres per hour
By how many acres will the fire grow between 6am and 10 am
Hours between (6 - 10) am = 6 hours
Take the integral of the rate function with upper limit = 6 and lower limit = 0
∫5√t dt at t = 6, t = 0
5∫√tdt = 5∫t^1/2 dt at t = 6, t = 0
5 (t^1/2 + 1 / 1/2 + 1) at t = 6, t = 0
5 ( t^3/2 / 3/2) at t = 6, t = 0
5 * 2/3 (t^3/2)
[10/3 *t^3/2] at t = 6, t = 0
(10/3 * 6^3/2) - (10/3 * 0^3/2)
(10/3 * 14.696938) - 0
48.989794
= 49 acres ( approximately)