Activity -question

Question

The Jones experienced a lot of snow this year. On Saturday, the snow was falling at the exponential rate of 10% per hour. The Jones originally had 2 inches of snow.

a. Write an exponential equation that models the inches of snow, S, on the ground at any given hour, h. (Recall that in general the exponential equation takes on the form of 𝐴 = 𝐴0𝑒 ^𝑏𝑡) Use the correct variables. S = ________

b. If the snow began at 8 A.M. on Saturday and the Jones are expected home Sunday at 9 P.M., approximately how many feet of snow rounded to the nearest feet, will they have to shovel from their driveway? _______ Is this enough to cancel school on Monday? __________

c. After about how many hours, will the snow be at least 2 feet?______ (Hint: ‘e’ can be found on your calculator right above the ‘ln’ function key. Be careful with conversion factors, ___ inches in 1 foot).

Answer 1

S = 2e^.1t

8am Saturday to 9pm Sunday = 37 hours

S=2e^.1(37) = 2e^3.7 = about 80.895 in. = 6.74 feet = 7 feet rounded to nearest integer

2 ft = 24 in. = 2e^.1t

24 = 2e^.1t

12 = e^.1t

take natural logs of both sides

ln12 = .1t

divide by .1

t = ln12/.1 = 10ln12 = 24.85 hours = 24 hours and about 51 minutes to get 2 feet of snow

if this happens in northern US, schools stay open

if it happens in the South where they aren't prepared for snow, schools need to close

but if you really start at 0 inches and snow increases at 10% per hour

then

A =0e^.1t

A= 0 inches forever

every hour 10% of 0 inches, compounded continuously is still zero for all eternity

in which case never close the schools even if the snow increased a billion percent per hour

or

A=0(e^.1t)

=0(e^.1(infinity))

= zero times infinity which is an indeterminate form