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Answer:
A) a = 1050 and b = 0.81
B) 3.3
Step-by-step explanation:
Original price of the computer = $ 1050
Rate of decrease in price = r = 19%
This means, every year the price of the computer will be 19% lesser than the previous year. In other words we can say that after a year, the price of the computer will be 81% of the price of the previous year.
Part A)
The exponential model is:
Here, a indicates the original price of the computer i.e. the price at time t = 0. So for the given case the value of a will be 1050
b represents the multiplicative rate of change i.e. the percentage that would be multiplied to the price of previous year to get the new price. For this case b would be 81% or 0.81
So, a = 1050 and b = 0.81
The exponential model would be:
Part B)
We have to find after how many years, the worth of the computer will be reduced to half. This means we have the value of v which is 1050/2 = $ 525
Using the exponential model, we get:
Taking log of both sides:
Thus, after 3.3 years the worth of computer will be half of its original price.