Algerbra 2 homework help: Exponentials and Logarithms?
I was sick and out of school the day of the lesson. Any help would be greatly appreciated! Also, if you can explain to me how you got the answers, so I can learn how to do it, that would be even better!
In 2004 Mr. Martin bought a Honda Civic for $19,200. In 2015 the car was valued at $4,300. Assuming normal wear and tear, calculate the following, showing all work:
a. The rate of depreciation.
b. The value of the car in 2017.
(HINT: This is exponential, not linear!)
A = p(1 - r)^t
4300 = 19200(1 - r)^(2015 - 2004)
4300 = 19200(1 - r)^11
divide both sides by 19200
0.2239583333 = (1 - r)^11
Take the log of both sides
-0.649832773188602 = 11log(1 - r)
Divide both sides by 11
-0.05907570665351 = log (1 - r)
Exponentiate both sides using 10 as the base
0.872819204398966 = 1 - r
Subtract 1 from both sides
-0.12718079560103 = -r
r 0.127
r 12.7% <-----
------------------
In 2017
a = p(1 - r)^t
a = 4300( 0.872819204398966)^(2017 - 2015)
a = 4300(0.872819204398966)^(2)
a $3,276 <
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