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Student: Kiare Mays Date: 06/15/20
Instructor: Valery Shemetov Course: MTH154 – Quantitative Reasoning (with MCR4)
Assignment: Section 6.2 Homework
Given the exponential equation , complete parts (a) through (b) below.y = 250 • e 0.0845 • x
(a) Represent as a decimal to 4 decimal places.e 0.0845
(Round to four decimal places as needed.)
(b) Rewrite the equation in the form .P = P • (1 + r)0 x
P = 250 • (1.0845)x
P = 250 • (1 + 8.82%)x
P = 250 • (0.0882)x
P = 250 • (1 + 8.45%)x
A population can be modeled by the exponential equation , where t years since 1990 and y population. Complete parts (a) through (d) below.
y = 250,000 • e − 0.0757 • t = =
(a) What is the continuous decay rate per year? (Hint: If the rate k is a negative number, this implies a continuous decay rate with the opposite sign of k.)
The population is decreasing at a continuous rate of % per year. (Round to two decimal places as needed.)
(b) What is the annual decay rate (not continuous)? (Hint: If the rate r is a negative number, this implies an annual decay rate with the opposite sign of r.)
The population is decreasing at an annual rate of % per year. (Round to two decimal places as needed.)
(c) Rewrite the equation in the form .P = P • (1 + r)0 t
A. P = 250,000 • (1 − 7.57%)t
B. P = 250,000 • (0.9243)t
C. P = 250,000 • ( − 0.729)t
D. P = 250,000 • (0.9271)t
(d) How many people will there be after 8 years?
people (Round to the nearest whole number as needed.)
3. A population can be modeled by the exponential equation , where t years since 2010 and y population. Complete parts (a) through (d) below.
y = 11,000 • e 0.2124 • t = =
(a) What is the continuous growth rate per year?
% (Round to two decimal places as needed.)
(b) What is the annual growth rate (not continuous)?
% (Round to two decimal places as needed.)
(c) Rewrite the equation in the form .P = P • (1 + r)0 t
A. P = 11,000 • (1.2124)t
B. P = 11,000 • (0.2366)t
C. P = 11,000 • (1 + 21.24%)t
D. P = 11,000 • (1 + 23.66%)t
(d) How many people will there be after 8 years?
people (Round to the nearest whole number as needed.)
4. Consider the following case of exponential growth. Complete parts a through c below.
The population of a town with an initial population of grows at a rate of % per year.48,000 7.5
a. Create an exponential function of the form , (where r 0 for growth and r 0 for decay) to model the situation described.
Q = Q (1 + r)0 × t > <
Q ( )= × t
(Type integers or decimals.)
b. Create a table showing the value of the quantity Q for the first 10 years of growth.
Year t= Population Year t= Population 0 48,000 6 1 7 2 8 3 9 4 10 5
(Round to the nearest whole number as needed.)
c. Make a graph of the exponential function. Choose the correct graph below.
A.
0 10 40,000
110,000
Year
Po pu
la tio
n
B.
0 10 30,000
100,000
Year
Po pu
la tio
n
C.
0 10 40,000
100,000
Year
Po pu
la tio
n
D.
0 10 20,000
100,000
Year
Po pu
la tio
n
5. Consider the following case of exponential decay. Complete parts (a) through (c) below.
A privately owned forest that had acres of old growth is being clear cut at a rate of % per year.5,000,000 2
a. Create an exponential function of the form , (where r 0 for growth and r 0 for decay) to model the situation described.
Q = Q (1 + r)0 × t > <
Q ( )= × t
(Type integers or decimals.)
b. Create a table showing the value of the quantity Q for the first 10 years of growth.
Year t= Acres Year t= Acres 0 5,000,000 6 1 7 2 8 3 9 4 10 5
(Round to the nearest whole number as needed.)
c. Make a graph of the exponential function. Choose the correct graph below.
A.
0 10 4,000,000
5,000,000
Year
Ac re
s
B.
0 10 0
1,000,000
Year
Ac re
s
C.
0 10 4,000,000
5,000,000
Year
Ac re
s
D.
0 10 4,000,000
5,000,000
Year
Ac re
s
6. Answer the questions for the problem given below. The average price of a home in a town was $ in 2007 but home prices are rising by % per year.179,000 3
a. Find an exponential function of the form (where r 0) for growth to model the situation described.Q = Q (1 + r)0 × t >
Q $ (1 )= × + t
(Type an integer or a decimal.)
b. Fill the table showing the value of the average price of a home for the following five years.
Year t= Average price 0 $179,000 1 $ 2 $ 3 $ 4 $ 5 $
(Do not round until the final answer. Then round to the nearest dollar as needed.)
7. Consider the following case of exponential growth. Complete parts (a) through (c) below.
Your starting salary at a new job is $ per month, and you get annual raises of % per year.1700 6
a. Create an exponential function of the form , (where r 0 for growth and r 0 for decay) to model the monthly salary situation described.
Q = Q (1 + r)0 × t > <
Q ( )= × t
(Type integers or decimals.)
b. Create a table showing the value of the quantity Q for the first 10 years of growth.
Year t= Salary (per month) Year t= Salary (per month) 0 $1700 6 $ 1 $ 7 $ 2 $ 8 $ 3 $ 9 $ 4 $ 10 $ 5 $
(Round to two decimal places as needed.)
c. Make a graph of the exponential function. Choose the correct graph below.
A.
0 10 0
800 1,600 2,400 3,200 4,000
Year
Sa la
ry (d
ol la
rs ) B.
0 10 0
800 1,600 2,400 3,200 4,000
Year
Sa la
ry (d
ol la
rs )
C.
0 10 0
800 1,600 2,400 3,200 4,000
Year
Sa la
ry (d
ol la
rs ) D.
0 10 0
800 1,600 2,400 3,200 4,000
Year
Sa la
ry (d
ol la
rs )
8.
9.
Air pressure can be modeled by the exponential equation , where x altitude in 1000's of feet and y air pressure in psi. Complete parts (a) through (e) below.
y = 14.1 • e − 0.0423 • x = =
(a) What is the continuous decay rate per 1000 feet? (Hint: If the rate k is a negative number, this implies a continuous decay rate with the opposite sign of k.)
The air pressure is decreasing at a continuous rate of % per 1000 feet. (Round to two decimal places as needed.)
(b) What is the decay rate every 1000 feet (not continuous)? (Hint: If the rate r is a negative number, this implies an annual decay rate with the opposite sign of r.)
The air pressure is decreasing at a rate of % per 1000 feet. (Round to two decimal places as needed.)
(c) Rewrite the equation in the form .P = P • (1 + r)0 x
A. P = 14.1 • (0.9586)x
B. P = 14.1 • (1.0414)x
C. P = 14.1 • (1 − 4.23%)x
D. P = 14.1 • (0.9577)x
(d) What is the air pressure at 35,000 feet?
psi (Round to two decimal places as needed.)
(e) What is the air pressure at sea level?
psi (Round to one decimal place as needed.)
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