MTH 252 | September 13, 2025
Scarlett Hill
Dr. Sharon Ramirez
MTH 252
Linear Algebra Exercises
With Solutions
Problem 1: A bacteria culture starts with 100 bacteria and grows exponentially at a rate of
6.0% per hour. Write the exponential function and find the population after 8 hours.
Solution:
Exponential growth model: P(t) = P₀ × (1 + r)^t
P(t) = 100 × (1 + 0.060)^t
P(t) = 100 × 1.060^t
After 8 hours:
P(8) = 100 × 1.060^8
P(8) = 100 × 1.594
P(8) = 159 bacteria
Problem 2: A cell phone plan costs 45.09 per month plus 4.94 per text message. If the total
cost is $147.66, find the number of text messages used.
Solution:
Let x = number of text messages
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
147.66 = 45.09 + 4.94x
Solving for x:
147.66 - 45.09 = 4.94x
102.57 = 4.94x
x = 102.57 ÷ 4.94
x = 20.8 text messages
Double-checking the work:
Check: 45.09 + 4.94(20.8) = 45.09 + 102.75 = 147.84 ✓
Note: The textbook example on page 294 shows a similar approach
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:43:09 GMT -05:00
https://www.coursehero.com/file/251540522/ALG-217-Algebra-Solutions-9371docx/
, MTH 252 | September 13, 2025
Problem 3: A gym membership has an enrollment fee of 64.67 and costs 0.97 per month. If
the total cost is $217.45, find the number of months used.
Solution:
Let x = number of months
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
217.45 = 64.67 + 0.97x
Solving for x:
217.45 - 64.67 = 0.97x
152.78 = 0.97x
x = 152.78 ÷ 0.97
x = 157.5 months
Step-by-step verification:
Check: 64.67 + 0.97(157.5) = 64.67 + 152.78 = 217.44 ✓
Problem 4: A rectangular garden has length (x + 8) meters and width (x + 6) meters.
Equation: Area = (x + 8)(x + 6) = 275 Find the value of x if the area is 275 square meters.
Solution:
Problem 5: Solve the logarithmic equation: log₍10₎(4x - 6) = 2
Solution:
Given: log₍10₎(4x - 6) = 2
Converting to exponential form:
4x - 6 = 10²
4x - 6 = 100
4x = 106
x = 106/4
x = 26.500
Double-checking the work:
Check: log₍10₎(4(26.500) - 6) = log₍10₎(100) = log₍10₎(10²) = 2 ✓
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:43:09 GMT -05:00
https://www.coursehero.com/file/251540522/ALG-217-Algebra-Solutions-9371docx/
Scarlett Hill
Dr. Sharon Ramirez
MTH 252
Linear Algebra Exercises
With Solutions
Problem 1: A bacteria culture starts with 100 bacteria and grows exponentially at a rate of
6.0% per hour. Write the exponential function and find the population after 8 hours.
Solution:
Exponential growth model: P(t) = P₀ × (1 + r)^t
P(t) = 100 × (1 + 0.060)^t
P(t) = 100 × 1.060^t
After 8 hours:
P(8) = 100 × 1.060^8
P(8) = 100 × 1.594
P(8) = 159 bacteria
Problem 2: A cell phone plan costs 45.09 per month plus 4.94 per text message. If the total
cost is $147.66, find the number of text messages used.
Solution:
Let x = number of text messages
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
147.66 = 45.09 + 4.94x
Solving for x:
147.66 - 45.09 = 4.94x
102.57 = 4.94x
x = 102.57 ÷ 4.94
x = 20.8 text messages
Double-checking the work:
Check: 45.09 + 4.94(20.8) = 45.09 + 102.75 = 147.84 ✓
Note: The textbook example on page 294 shows a similar approach
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:43:09 GMT -05:00
https://www.coursehero.com/file/251540522/ALG-217-Algebra-Solutions-9371docx/
, MTH 252 | September 13, 2025
Problem 3: A gym membership has an enrollment fee of 64.67 and costs 0.97 per month. If
the total cost is $217.45, find the number of months used.
Solution:
Let x = number of months
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
217.45 = 64.67 + 0.97x
Solving for x:
217.45 - 64.67 = 0.97x
152.78 = 0.97x
x = 152.78 ÷ 0.97
x = 157.5 months
Step-by-step verification:
Check: 64.67 + 0.97(157.5) = 64.67 + 152.78 = 217.44 ✓
Problem 4: A rectangular garden has length (x + 8) meters and width (x + 6) meters.
Equation: Area = (x + 8)(x + 6) = 275 Find the value of x if the area is 275 square meters.
Solution:
Problem 5: Solve the logarithmic equation: log₍10₎(4x - 6) = 2
Solution:
Given: log₍10₎(4x - 6) = 2
Converting to exponential form:
4x - 6 = 10²
4x - 6 = 100
4x = 106
x = 106/4
x = 26.500
Double-checking the work:
Check: log₍10₎(4(26.500) - 6) = log₍10₎(100) = log₍10₎(10²) = 2 ✓
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:43:09 GMT -05:00
https://www.coursehero.com/file/251540522/ALG-217-Algebra-Solutions-9371docx/
