A forest fire is found at midnight. It covers 1200 acres then. It is spreading at a rate of f(t)= 5√t acres per hour. By how many acres will the fire grow between ​6:00 am and​ 10:00 am? Between ​6:00 am and​ 10:00 am the fire will grow by acres.

49 acres

Step-by-step 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)