Question

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 functi

Exponential models
ANSWERED
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.

Answers (1)

2021-05-08

Deternmine the multiplier. Since 2005 is the start, this will be 0. The point will be (0,60).
\(\displaystyle{y}={a}{b}^{{x}}\) Write the equation
\(\displaystyle{60}={a}{b}^{{0}}\) Substitute the values
\(60=a(1)\) Use zero rule of exponent
\(60=a\) Simplify
In order to determine b, use point (5,45) for 2010.
\(\displaystyle{y}={a}{b}^{{x}}\) Write the equation
\(\displaystyle{45}={60}{\left({b}\right)}^{{5}}\) Substitute the values
\(\displaystyle\frac{{45}}{{65}}={60}\frac{{\left({b}\right)}^{{5}}}{{60}}\) Divide both sides by 60
\(0.75=b^5\) Simplify
\(\displaystyle{5}\sqrt{{0.75}}={5}\sqrt{{b}}^{{5}}\) Use radical to remove exponent
0.944=b Simplify
The multiplier is 0.944. Subtract the multiplier from 1 to determine the percent decrease. 1-0.944=0.056= 5.6%
The exponential function for the given situation is: \(\displaystyle{f{{\left({x}\right)}}}={60}{\left({0.944}\right)}^{{x}}\)
Using the exponential function, \(\displaystyle{f{{\left({x}\right)}}}={60}{\left({0.944}\right)}^{{x}}\), determine the value in 2020, which is 15 years from 2005.
\(\displaystyle{f{{\left({x}{0}\right)}}}={60}{\left({0.944}\right)}^{{x}}\) Write the function
\(\displaystyle{f{{\left({15}\right)}}}={60}{\left({0.944}\right)}^{{15}}\) Substitute the values
\(f(15)=25.28\) Perform operation

0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

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 2021-05-26
You open a bank account to save for college and deposit $400 in the account. Each year, the balance in your account will increase \(5\%\). a. Write a function that models your annual balance. b. What will be the total amount in your account after 7 yr? Use the exponential function and extend the table to answer part b.
asked 2021-05-12
When a < 0 and b>1,y=abx models negative exponential growth. a. Write an exponential function that models negative growth. b. Give an example of a situation that could be modeled by your function. c. Explain one difference between negative exponential growth and exponential decay.
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.
...