Tina and Boyang docide to, invest in 817650. They want t Brewster County, Texas.

Question

Tina and Boyang docide to, invest in 817650. They want t Brewster County, Texas. rice was 88825 Only 20 days later, on 15 December 2017, the price Noveuber 2017, tiue o use any money they might make to visit Big Bend National Park in Biteoin. They find that on 25 Novemuber 20T, t ho (a) Find the value of the growth/decay constant k. Round your aniwer to 4 deima places. (6 pts.) (b) Use your answer from part (a) to write the exponential growth/decay model, amount amount A as a function of time t, for this case. Which date corresponds to 1 = 0 in your model? (4 pts.) find how many daysepast t 0 will be required to hit this point. Round your answer to the nearest whole number. (5 pts.) (c) Tina and Boyang want to know when Bitcoin will hit 81,000,000. Use your model to night have been. Use your model to find how many days before t0 he would have made this purchase. Round your answer to the nearest whole mumber. (5 pts.) (d) They heard their professor say that he bought in at $400 and want to know when that

Explanation / Answer

general exponential growth equation is A(t)=Petk

(a)

A(20)=17650,P=8825, t=20

=>17650=8825e20k

=>e20k=17650/8825

=>e20k=2

=>20k=ln(2)

=>k=(1/20)ln(2)

=>k=0.0347 per day

(b)

A(t)=8825e((1/20)ln(2))t

A(t)=8825e0.0347t

t =0 corresponds to 25 november 2017

(c)

A(t) =1000000

=>8825e((1/20)ln(2))t=1000000

=>e((1/20)ln(2))t=(1000000/8825)

=>((1/20)ln(2))t=ln(1000000/8825)

=>t =136.48

137 days past t=0 are required to hit this point

(d)

A(t) =400

=>8825e((1/20)ln(2))t=400

=>e((1/20)ln(2))t=(400/8825)

=>((1/20)ln(2))t=ln(400/8825)

=>t =-89.27

89 days before t=0 he would have made this purchase

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