1. Depreciation The value of a 2003 Toyota Corolla is given by the function v(t)
ID: 3147552 • Letter: 1
Question
1. Depreciation The value of a 2003 Toyota Corolla is given by the function
v(t) = 14000(0.93) ^t
where t is the number of years since its purchase and v(t) is its value in dollars. (Source: Kelley Blue Book)
a. What was its initial purchase price?
b. What percentage of its value does the Toyota Corolla lose each year?
c. How long will it take for the value of the Toyota Corolla to reach $12,000?
2.Physics Plutonium is a radioactive element which has a half-life of 24,360 years. The half-life of a radioactive substance is the time it takes for half of the substance to decay. Find an exponential function of the form Ae kt that gives the amount of plutonium left after t years if the initial amount of plutonium is 10 pounds. How long will it take for the plutonium to decay to 2 pounds?
Explanation / Answer
given v(t)=14000(0.93)t
v(t)=14000(1-7/100)t
intial purchase price t=0
v(t)=14000(1-7/100)0=14000*1=14000
v(t)=v0(1-d/100)t
d=7%
7 percentage of its value does the Toyota Corolla lose each year
v(t)=14000*0.93t
12000=14000*0.93t
12000/14000=0.93t
0.857142857=0.93t
apply log on both sides
log(0.857142857)=tlog(0.93)
t=log(0.857142857)/log(0.93)
t=2.12414508years
it take 2.124 years for the value of the Toyota Corolla to reach $12,000
as per chegg rules and policy 1 st question is answered
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