U.S. patents. The number of applications for patents, N , grew dramatically in recent years, with growth averaging about 5.8% per year. That is, N ' ( t ) = 0.058 N ( t ) . ( Source : Based on data from the U.S. Patent and Trademark office, 2009–2013.) a. Find the function that satisfies the equation. Assume that t = 0 corresponds to 2009, when approximately 483,000 patent applications were received. b. Estimate the number of patent applications in 2020. c. Estimate the doubling time for N ( t ) .
U.S. patents. The number of applications for patents, N , grew dramatically in recent years, with growth averaging about 5.8% per year. That is, N ' ( t ) = 0.058 N ( t ) . ( Source : Based on data from the U.S. Patent and Trademark office, 2009–2013.) a. Find the function that satisfies the equation. Assume that t = 0 corresponds to 2009, when approximately 483,000 patent applications were received. b. Estimate the number of patent applications in 2020. c. Estimate the doubling time for N ( t ) .
U.S. patents. The number of applications for patents, N, grew dramatically in recent years, with growth averaging about 5.8% per year. That is,
N
'
(
t
)
=
0.058
N
(
t
)
.
(Source: Based on data from the U.S. Patent and Trademark office, 2009–2013.)
a. Find the function that satisfies the equation. Assume that
t
=
0
corresponds to 2009, when approximately 483,000 patent applications were received.
b. Estimate the number of patent applications in 2020.
Births to Unmarried Mothers The percent of livebirths to unmarried mothers for the years 1970–2007can be modeled by the logistic functiony = 44.742/1 + 6.870e-0.0782xwhere x is the number of years after 1960.a. Use this model to estimate the percent in 1990 andin 1996.b. What is the upper limit of the percent of teenmothers who were unmarried, according to thismodel?
At the beginning of the last decade, a total of 7.2 million passengers took a cruise vacation.
The global cruising industry has been growing at approximately 7% per year.
Assume that this growth rate continues.
Suppose N = (t) gives the number of passengers, in millions, that take a cruise vacation at year t.
Answer parts (a), (b), (c), and (d) of the question. Click VERIFY to move to the next part.
(a) Report the following. Use the pull-down menu to indicate the units.
A0) = Number
Click for List
(b) If (t) is written in the form a-b’, do you predict the value of b to be greater than 1 or less than 1?
O b is greater than 1 O b is less than 1
(c) Complete the boxes below to write a formula which gives N as a function of t, where t is in years.
Do not round any values. Since your formula gives N in millions of people,
check that it passes through the initial value x = 0, N= 7.2, as opposed to passing through x = 0, y = 7,200,000.
N=
Number
( Number
(d) How many millions of cruise…
2)
An initial investment of $10,000 grows at 11% per year. What function represents the value of the investment after t years?
R) - 10,000(1.11)
R) - 10,000(1.11)
- 10,000(11)'
A) – 10,000(0.11)'
a.
c.
b.
d.
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