The function f ( x ) = 2.9 x + 20.1 models the median height, f(x), in inches, of boys who are x months of age. The graph of is shown. a. Describe how the graph can be obtained using transformations of the square root function f ( x ) = x . b. According to the model, what is the median height of boys who are 48 months, or four years, old? Use a calculator and round to the nearest tenth of an inch. The actual median height for boys at 48 months is 40.8 inches. How well does the model describe the actual height? c. Use the model to find the average rate of change, in inches per month, between birth and 10 months. Round to the nearest tenth. d. Use the model to find the average rate of change, in inches per month, between 50 and 60 months. Round to the nearest tenth. How does this compare with your answer in part (c)? How is this difference shown by the graph?
The function f ( x ) = 2.9 x + 20.1 models the median height, f(x), in inches, of boys who are x months of age. The graph of is shown. a. Describe how the graph can be obtained using transformations of the square root function f ( x ) = x . b. According to the model, what is the median height of boys who are 48 months, or four years, old? Use a calculator and round to the nearest tenth of an inch. The actual median height for boys at 48 months is 40.8 inches. How well does the model describe the actual height? c. Use the model to find the average rate of change, in inches per month, between birth and 10 months. Round to the nearest tenth. d. Use the model to find the average rate of change, in inches per month, between 50 and 60 months. Round to the nearest tenth. How does this compare with your answer in part (c)? How is this difference shown by the graph?
Solution Summary: The author explains the steps of obtaining the graph of the function f(x)=2.9sqrtx+20.1 using transformation.
The function
f
(
x
)
=
2.9
x
+
20.1
models the median height, f(x), in inches, of boys who are x months of age. The graph of is shown.
a. Describe how the graph can be obtained using transformations of the square root function
f
(
x
)
=
x
.
b. According to the model, what is the median height of boys who are 48 months, or four years, old? Use a calculator and round to the nearest tenth of an inch. The actual median height for boys at 48 months is 40.8 inches. How well does the model describe the actual height?
c. Use the model to find the average rate of change, in inches per month, between birth and 10 months. Round to the nearest tenth.
d. Use the model to find the average rate of change, in inches per month, between 50 and 60 months. Round to the nearest tenth. How does this compare with your answer in part (c)? How is this difference shown by the graph?
Compare the interest earned from #1 (where simple interest was used) to #5 (where compound interest was used). The principal, annual interest rate, and time were all the same; the only difference was that for #5, interest was compounded quarterly. Does the difference in interest earned make sense? Select one of the following statements. a. No, because more money should have been earned through simple interest than compound interest. b. Yes, because more money was earned through simple interest. For simple interest you earn interest on interest, not just on the amount of principal. c. No, because more money was earned through simple interest. For simple interest you earn interest on interest, not just on the amount of principal. d. Yes, because more money was earned when compounded quarterly. For compound interest you earn interest on interest, not just on the amount of principal.
Compare and contrast the simple and compound interest formulas. Which one of the following statements is correct? a. Simple interest and compound interest formulas both yield principal plus interest, so you must subtract the principal to get the amount of interest. b. Simple interest formula yields principal plus interest, so you must subtract the principal to get the amount of interest; Compound interest formula yields only interest, which you must add to the principal to get the final amount. c. Simple interest formula yields only interest, which you must add to the principal to get the final amount; Compound interest formula yields principal plus interest, so you must subtract the principal to get the amount of interest. d. Simple interest and compound interest formulas both yield only interest, which you must add to the principal to get the final amount.
Sara would like to go on a vacation in 5 years and she expects her total costs to be $3000. If she invests $2500 into a savings account for those 5 years at 8% interest, compounding semi-annually, how much money will she have? Round your answer to the nearest cent. Show you work. Will she be able to go on vacation? Why or why not?
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