I Need Help with Math Problem!

Question

Suppose a substance grows at a rate of 26.9 % per hour and begins with 147 cells.

A) The equation that models this scenario is Q_t =  Blank 1. Calculate the answer by read surrounding text. * (  Blank 2. Calculate the answer by read surrounding text. )^t. (Note, the part inside the parentheses must be simplified.) Do not round.

B ) How much will be present after 8 hours? Round to the nearest whole number.    Blank 3. Calculate the answer by read surrounding text. cells

C) After 3 days? Round to the nearest whole number.     Blank 4. Calculate the answer by read surrounding text. cells

D) How long will it take for there to be 1,000,000 cells? Round to one decimal place.   Blank 5. Calculate the answer by read surrounding text. hours

E) What is the doubling time of this substance?    Blank 6. Calculate the answer by read surrounding text. hours

Answer 1

Q(h)=147e^.269h where h= hours

Q(8) = 147e^.269(8) = 1,265 after 8 hours

Q(3 days) = Q(3(24) = Q(72) = 147e^.269(72) = 147e^19.368

=37,908,173,550

= about 38 billion in 3 days

1,000,000 = 47e^.269h

1,000,000/47 =e^.269h

take natural logs of both sides

ln(1000,000/147) = .269h

h = ln(1,000,000/147)/.269 = 32.8 hours to reach 1 million