Question

Suppose the retail of an automobile is $33,000 in 1999 and that it increases at 6% per year. a. Write the equation of the exponential function, in the form y=a(1+r)^t, that models the retail prrice of the automobile in 2014. b. Use the model to predict the retail price of the automobile in 2014.

Exponential models
ANSWERED
asked 2020-12-07
Suppose the retail of an automobile is $33,000 in 1999 and that it increases at 6% per year.
a. Write the equation of the exponential function, in the form \(\displaystyle{y}={a}{\left({1}+{r}\right)}^{{t}}\), that models the retail prrice of the automobile in 2014.
b. Use the model to predict the retail price of the automobile in 2014.

Answers (1)

2020-12-08
a) The retail price of automobile is $33,000 in the year 1999.
The price increases by 6% per year.
The given exponential function is \(\displaystyle{y}={a}{\left({1}+{r}\right)}^{{t}}\), where t is the years after 1999.
Substitute the given values in the exponential function as follows.
\(\displaystyle{P}{\left({t}\right)}={33},{000}{\left({1}+{6}\%\right)}^{{t}}\)
\(\displaystyle{P}{\left({t}\right)}={33},{000}{\left({1}+{0.06}\right)}^{{t}}\)
\(\displaystyle{P}{\left({t}\right)}={33},{000}{\left({1.06}\right)}^{{t}}\)
Thus, the function that models the retail price of automobile is
\(\displaystyle{P}{\left({t}\right)}={33},{000}{\left({1.06}\right)}^{{t}}\)
Therefore, the correct answer is second option.
b) From (a), the function that models the retail price of automobile is \(\displaystyle{P}{\left({t}\right)}={33},{000}{\left({1.06}\right)}^{{t}}\) where t is the years after 1999.
The given year is 2014
So, the value of t is 2014-1999=5.
Evaluate the retail price of the automobile in 2004 as follows.
\(\displaystyle{P}{\left({t}\right)}={33},{000}{\left({1.06}\right)}^{{5}}\)
\(\displaystyle{P}{\left({5}\right)}={33},{000}{\left({1.33822}\right)}\)
\(\displaystyle{P}{\left({5}\right)}={44161.4406}\)
\(\displaystyle{P}{\left({5}\right)}\approx{44},{161}\)
Therefore, the price of the automobile in the year 2004 is about $44,161.
0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2021-05-07
A share of ABC stock was worth $60 in 2005 and only worth $45 in 2010. a. Find the multiplier and the percent decrease. b. Write an exponential function that models the value of the stock starting from 2005. c. Assuming that the decline in value continues at the same rate , use your answer to (b) to predict the value in 2020.
asked 2021-05-17
Models that increase or decrease by a percentage will be exponential. Which of the following scenarios will use exponential modeling?
A) A person makes $50,000 per year and then has a salary increase of $6,000 for each year of experience.
B) A person makes $50,000 per year and their salary will increase by 2.5% each year.
asked 2021-05-16
A computer valued at $1500 loses 20% of its value each year. a. Write a function rule that models the value of the computer. b. Find the value of the computer after 3 yr. c. In how many years will the value of the computer be less than $500? Use the exponential function to answer part b.
asked 2021-06-02
The table shows the populations P (in millions) of the United States from 1960 to 2000. Year 1960 1970 1980 1990 2000 Popupation, P 181 205 228 250 282
(a) Use the 1960 and 1970 data to find an exponential model P1 for the data. Let t=0 represent 1960. (c) Use a graphing utility to plot the data and graph models P1 and P2 in the same viewing window. Compare the actual data with the predictions. Which model better fits the data? (d) Estimate when the population will be 320 million.
...