Question

20.

Answer 1

Answer:

a) e-0.03x(0.3-0.009x)

b) 33 hrs 20 min

c) 17.182

Step-by-step explanation:

Taking derivative of the above equation would give us the rate for change in donations :

hence

f'(x) = d/dx (0.3xe-0.03x)

using product rule of derivation where (uv)' = u'v +v'u

hence

f'(x) = (e-0.03x)d/dx(0.3x) + 0.3x*d/dx(e-0.03x)

       = 0.3e-0.03x + 0.3x(-0.03)(e-0.03x)

  f'(x)   =0.3e-0.03x -0.009xe-0.03x

hence

a) rate of change in donations = e-0.03x(0.3-0.009x) taking exponent common

b) f'(x) = 0 according to statement

hence 0 = e-0.03x(0.3-0.009x)

     0 = 0.3 - 0.009 x

which gives x = 33.33 hrs i.e after 33 hrs and 20 minutes rate of change of donations is 0.

c) donation level at the time is given by

f(x) = 0.3xe-0.03x

f(33.33) = 0.3 (33.33)e-0.03(33.33)

              = 17.182

That is 17.182 thousand donations were made at that time.