College Algebra – (MAC1105)Keystone SLO: Solve applications problems involving exponential and logarithmic functions.
Keystone SLO Assessment: Homework in week 7
Standard: Quantitative Literacy (QL)
Exercise 1:
You have two options for investing $500. The first earns 7% interest compounded annually, and the
second earns 7% simple interest. The figure shows the growth of each investment over a 30 years
period.
a. What is the approximate amount of money in your account, after 15 years, for the linear model?
Explain
b. What is the approximate amount of money in your account, after 20 years, for the exponential
model? Explain
c. How much more money is, approximately, in your account for the exponential model than for
the linear model, after 30 years? How did you calculate this amount?
Exercise 2:
You will deposit $500 in a bank account at a 7% interest compounded annually. The formula for
compound interest is shown below:
𝑟 𝑛𝑡
𝐴(𝑡) = 𝑃 (1 + )
𝑛
a. Select the values of P, r, and n from the problem statement.
b. If you graph t vs. A, will the graph be increasing, decreasing or constant? Explain.
c. Write the formula that describe the data given.
Exercise 3:
You will deposit $3000 in a bank account at a 2% interest compounded monthly. The formula for
compound interest is shown below:
𝑟
𝐴(𝑡) = 𝑃(1 + )𝑛𝑡
𝑛
a. Select the value of P, r and n from the problem statement.
b. Explain the order in which you will perform the operations to calculate A(t).
c. What will be the amount in the bank account after 4 years?
Exercise 4:
You have two options for investing $500. The first earns 7% interest compounded annually, and the
second earns 7% simple interest. The figure shows the growth of each investment over a 30 years
period.
a. Determine which graph represents each type of investment. Explain your reasoning.
b. Which option would you choose? Explain
c. Just based on the information provided by the graph (without any calculation), can you estimate
the amount of money in you 7% interest compounded annually account after 45 years? Explain.
Final Investment Value using Simple Interest formula: 𝐴(𝑡) = 𝑃(1 + 𝑟𝑡)
𝑟 𝑛𝑡
Final Investment Value using Compounded Interest formula: 𝐴(𝑡) = 𝑃 (1 + 𝑛)
Exercise 5:
The exponential growth model for a population contains certain assumptions, example:
1.
2.
3.
4.
There is constant rate of birth and death among the individuals of the population.
There is no immigration and emigration-taking place in the population.
There are no genetic variations among the individuals of the population.
Variations in age and size among population members are not included
a. Explain how failing to make these assumptions will affect your exponential growth model (use at
least two of the assumptions above).
The formula for the exponential growth model is: 𝐴 = 𝐴0 𝑒 𝑘𝑡 , where:
𝐴0 – original size.
k – constant representing the growth rate.
t – amount of time
Exercise 6:
From 1950 to 2010, the world population increased in 165% approximately.
The data presented below supports the above statement. The data is presented in three different forms
(table, set of ordered pairs, and a scatter plot graph).
a. Is the statement above correct, based on the data provided? Explain.
b. What format(s) could you use in a presentation to support the above statement? Explain your
selection.
c. What format(s) let you identify better the trend line that better fit the data (linear, exponential,
logarithmic, polynomial, etc.)? Explain your selection.
a. Table:
x, year
1950
1960
1970
1980
1990
2000
2010
y, world population
(billions)
2.6
3.0
3.7
4.5
5.3
6.1
6.9
b. Set of ordered pairs:
{(1950, 2.6), (1960, 3.0), (1970, 3.7), (1980, 4.5), (1990, 5.3), (2000, 6.1), (2010, 6.9)}
(x, y) = (year, population in billions).
c. Graph:
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