Question

Florida observed a greater annual rain fall. On Monday, the rain fell at the exponential rate of 10% hourly. Florida originally had 2 inches of rain.

I. Write an exponential equation that models the inches of rain, R, on the ground at any given hour, h. [exponential equation is expressed by A=Av0e^bt]  Consider variables.

II. The rain started 8 A.M. Monday and ended Tuesday at 9 P.M. About how many feet of rain rounded to the nearest feet, will have accrued?

III. How many hours will it take for the rain be at least 2 feet?

Answer 1

Given data is :

Rate of rain hourly, b =10%=0.1

Initial rain ,A₀ = 2 inch.

1) Exponential model: A=A₀ e^bt. where,t =time in hours and 'A' is the rain (in inches) at 't' hours.

2)The rain started 8 A.M. Monday and ended Tuesday at 9 P.M,

So total duration, t = 37 hours.

Therefore A=A₀ e^bt. substituting A₀ = 2 inch, b =10%=0.1 and t = 37 hours.

A=2*e^0.1*37=80.895 inches=6.7411 feets   (Since 1 foot =12 inch)

The rain started 8 A.M. Monday and ended Tuesday at 9 P.M,Amount of Rain is 7 ft.

3)Duration in hours to rain atleast 2 ft.

A= 2 ft=2*12=24 inches.

Now , A=A₀ e^bt. substituting A₀ = 2 inch, b =10%=0.1 and A= 24 inches.

finding 't' from 24=2*e^0.1*t

Therefore, t=ln(12)/0.1=24.85 hrs.

Duration in hours to rain atleast 2 ft is 25 hours.