The relative growth rate for a certain type of mutual fund is 5.1% per year. An account is opened with a balance of $35,000. How much is the mutual fund worth in 5 years? In your final answer, include all of your calculations.
Ceasar opens a bank account and makes an initial deposit of $1,800. The banker tells Ceasar that he is going to receive an annual rate of 3.2% on his investment. What is the balance of the account after one year, assuming that Ceasar doesn’t make any additional deposits or withdrawals?
A show pony weighs at least 900 pounds. After a recent weigh-in, the owner of a show pony amended the diet of his pony, increasing the animal's caloric intake, with the hope that the pony would gain weight to be shown in a few months. The data shown in the table and scatter plot below represents the pony's additional daily caloric intake and recorded weight gain (in pounds) of the show pony over the last ten weeks.
Additional Daily Calories Consumed
Weight Gained
(in pounds)
1,500
3
1,575
7
1,650
3
1,725
4
1,800
8
1,875
9
1,950
13
2,025
7
2,100
17
2,175
15
Part A: Use the data shown in the table and scatter plot to create an approximate equation for the line of best fit.
Part B: Incomplete sentences describe the show pony's weight gain in terms of the units used in the data.
Part C: According to the equation for the best fit line for the data, approximately how much weight would you expect the pony to gain in a week if its additional daily caloric intake for that week is 2,300 calories?
Hoping to increase pizza sales on Tuesdays, a new pizza restaurant prints and disperses the following coupon through email and fliers in a neighborhood marketing magazine
After ten weeks of the coupon offer, the owner of the restaurant needs to decide if the restaurant should continue to run the same special or offer a new one. Use the data collected in the table to determine whether or not the coupon appears to be generating sales for the restaurant.
Week
Total
Sales
1
$859
2
$1,176
3
$1,480
4
$1,365
5
$1,576
6
$1,498
7
$1,180
8
$1,964
9
$1,634
10
$1,580
Part A: Create a scatter plot and the line of best fit to represent the data in the table. Be sure to label each axis, as well as to include the proper titles for the scatter plot.
Part B: Use the total sales for weeks 4 and 9 to write an equation for the line of best fit. In your final answer, include all of your calculations.
Part C: in terms of the slope of the equation for the line of best fit, explain whether or not you think the coupon is responsible for the restaurant's increase or decrease in pizza sales on Tuesdays. Use complete sentences in your answer.
Part D: Assuming that the pizza restaurant wishes to continue the coupon for an additional five weeks, use the equation for the line of best fit to predict the restaurant's sales for the Tuesday of the 15th week.
how to work all of these out
To calculate the value of a mutual fund after a certain number of years, you can use the formula for compound interest:
Future Value = Principal * (1 + Growth Rate)^Number of Years
For the first question:
1. Convert the growth rate from a percentage to a decimal: 5.1% = 0.051.
2. Plug the values into the formula: Future Value = $35,000 * (1 + 0.051)^5.
3. Calculate the future value: Future Value = $35,000 * (1.051)^5 = $42,295.35.
For the second question:
1. Convert the annual interest rate from a percentage to a decimal: 3.2% = 0.032.
2. Calculate the balance after one year: Balance = $1,800 * (1 + 0.032) = $1,857.60.
For the third question, let's first create a table to observe the relationship between additional daily calories consumed and weight gained.
Additional Daily Calories Consumed | Weight Gained (in pounds)
1,500 | 3
1,575 | 7
1,650 | 3
1,725 | 4
1,800 | 8
1,875 | 9
1,950 | 13
2,025 | 7
2,100 | 17
2,175 | 15
To find the line of best fit, we can use a regression analysis or plot the scatter plot and fit a straight line through the data points.
Part A: By plotting the scatter plot, we can visually approximate the line of best fit.
Part B: The relationship between additional daily calories consumed and weight gained can be described as follows: As the additional daily calories consumed increases, the weight gained generally increases.
Part C: According to the equation for the best fit line, you can use the line to estimate the weight gain for a given additional daily caloric intake. In this case, if the additional daily caloric intake is 2,300 calories, you can estimate the weight gain by finding the corresponding point on the line of best fit.
For the fourth question, we need to analyze the data to determine if the coupon is generating sales for the restaurant.
Part A: Create a scatter plot using the given data. Label the x-axis as "Week" and the y-axis as "Total Sales". Include proper titles for the scatter plot.
Part B: To find the equation for the line of best fit, we can use the total sales from weeks 4 and 9. For those weeks, the total sales are $1,365 and $1,634. We can then find the equation for the line of best fit using these two points.
1. Calculate the slope of the line using the formula: Slope = (y2 - y1) / (x2 - x1) = ($1,634 - $1,365) / (9 - 4) = $269 / 5 = $53.80.
2. Substitute one of the points and the slope into the equation y = mx + b and solve for b:
$1,365 = $53.80(4) + b
$1,365 = $215.20 + b
b = $1,365 - $215.20 = $1,149.80.
3. The equation for the line of best fit is: y = $53.80x + $1,149.80.
Part C: The slope of the equation for the line of best fit ($53.80) represents the change in sales for each unit increase in week number. If the slope is positive, it suggests that the coupon is responsible for the increase in sales on Tuesdays. If the slope is negative, it suggests that the coupon may be causing a decrease in sales on Tuesdays.
Part D: To predict the sales for the 15th week, substitute x = 15 into the equation for the line of best fit:
y = $53.80(15) + $1,149.80
y = $807 + $1,149.80
y ≈ $1,956.80.