For much of the 20th century, new car prices rose at an average annual rate of...
For much of the 20th century, new car prices rose at an average annual rate of 5.89%. Given a beginning new car price of $900, how long did it take for the average new car price to rise to $27,865? Please round to the nearest year.
Homework Answers
The initial price of the car price is P0 = $900.
The final price of the car price is Pn = $27,865.
Where, n is the number of years in which this increase in the average car prices happened.
Given annual rate, r at which the car prices rose is 5.89%.
We know that, Final value = Initial value * ( 1 + r% )n
Therefore, on substituting in the above formula we get:
27,865 = 900 * (1+0.0589)n
27,865 / 900 = (1.0589)n
30.96 = (1.0589)n
Applying log on both sides.
log(30.96) = log(1.0589n)
We know that logab = b * loga
Therefore, log(30.96) = n * log(1.0589)
Here, n = log(30.96) / log(1.0589)
Substituting the logarithmic values in the above equation:
n = 1.491 / 0.0248
n = 60
Therefore, it took 60 years in 20th century for the average car prices to rise from $900 to $27,865.
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