Data from a 20-yr study show the number of new AIDS cases diagnosed among 20- to 24-yr-olds in the United States x years after the study began. a. Approximate the interval(s) over which the number of new AIDS cases among 20- to 24-yr-olds increased. b. Approximate the interval(s) over which the number of new AIDS cases among 20- to 24-yr-olds decreased. c. How many turning points does the graph show? d. Based on the number of turning points, what is the minimum degree of a polynomial function that could be used to model the data? Would the leading coefficient be positive or negative? e. How many years after the study began was the number of new AIDS cases among 20- to 24-yr-olds the greatest? f. What was the maximum number of new cases diagnosed in a single year?
Data from a 20-yr study show the number of new AIDS cases diagnosed among 20- to 24-yr-olds in the United States x years after the study began. a. Approximate the interval(s) over which the number of new AIDS cases among 20- to 24-yr-olds increased. b. Approximate the interval(s) over which the number of new AIDS cases among 20- to 24-yr-olds decreased. c. How many turning points does the graph show? d. Based on the number of turning points, what is the minimum degree of a polynomial function that could be used to model the data? Would the leading coefficient be positive or negative? e. How many years after the study began was the number of new AIDS cases among 20- to 24-yr-olds the greatest? f. What was the maximum number of new cases diagnosed in a single year?
Data from a 20-yr study show the number of new AIDS cases diagnosed among 20- to 24-yr-olds in the United States x years after the study began.
a. Approximate the interval(s) over which the number of new AIDS cases among 20- to 24-yr-olds increased.
b. Approximate the interval(s) over which the number of new AIDS cases among 20- to 24-yr-olds decreased.
c. How many turning points does the graph show?
d. Based on the number of turning points, what is the minimum degree of a polynomial function that could be used to model the data? Would the leading coefficient be positive or negative?
e. How many years after the study began was the number of new AIDS cases among 20- to 24-yr-olds the greatest?
f. What was the maximum number of new cases diagnosed in a single year?
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
College Algebra with Modeling & Visualization (5th Edition)
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