Beginning on January 1, park rangers in Everglades National Park began recording the water level for one particularly dry area of the park. The water level was initially 2.5 ft and decreased by approximately 0.015 ft/day. a. Write a function representing the water level L x (in ft), x days after January 1. b. Write an equation for L − 1 x . c. What does the inverse handier, represent in the context of this problem? d. Evaluate L − 1 1.9 and interpret its meaning in context.
Beginning on January 1, park rangers in Everglades National Park began recording the water level for one particularly dry area of the park. The water level was initially 2.5 ft and decreased by approximately 0.015 ft/day. a. Write a function representing the water level L x (in ft), x days after January 1. b. Write an equation for L − 1 x . c. What does the inverse handier, represent in the context of this problem? d. Evaluate L − 1 1.9 and interpret its meaning in context.
Solution Summary: The author determines the function L(x) ( in ft ) which defines the water level x days after January 1.
Beginning on January 1, park rangers in Everglades National Park began recording the water level for one particularly dry area of the park. The water level was initially 2.5 ft and decreased by approximately 0.015 ft/day.
a. Write a function representing the water level
L
x
(in ft), x days after January 1.
b. Write an equation for
L
−
1
x
.
c. What does the inverse handier, represent in the context of this problem?
d. Evaluate
L
−
1
1.9
and interpret its meaning in context.
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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