Consider the functions in Exercises 5–8 as representing the value of an ounce of palladium in U.S. dollars as a function of the time t in days. Find the average rates of change of R ( t ) over the time intervals [ t , t + h ] , where t is as indicated and h = 0 , 0.1 , and 0.01 days. Hence, estimate the instantaneous rate of change of R at time t, specifying the units of measurement. (Use smaller values of h to check your estimates.) [ HINT: See Example 1.] R ( t ) = 60 + 50 t − t 2 ; t = 5
Consider the functions in Exercises 5–8 as representing the value of an ounce of palladium in U.S. dollars as a function of the time t in days. Find the average rates of change of R ( t ) over the time intervals [ t , t + h ] , where t is as indicated and h = 0 , 0.1 , and 0.01 days. Hence, estimate the instantaneous rate of change of R at time t, specifying the units of measurement. (Use smaller values of h to check your estimates.) [ HINT: See Example 1.] R ( t ) = 60 + 50 t − t 2 ; t = 5
Solution Summary: The author calculates the average rate of change for the function R(t)=60+50t-t
Consider the functions in Exercises 5–8 as representing the value of an ounce of palladium in U.S. dollars as a function of the time t in days. Find the average rates of change of
R
(
t
)
over the time intervals
[
t
,
t
+
h
]
, where t is as indicated and
h
=
0
,
0.1
,
and 0.01 days. Hence, estimate the instantaneous rate of change of R at time t, specifying the units of measurement. (Use smaller values of h to check your estimates.) [HINT: See Example 1.]
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) =…
Elementary Algebra For College Students (10th Edition)
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