Question

Calculate had a net income of 8 million dollars in 2010, while a small competing company, Computate, had a net income of 3 millions dollars. The management of Calculate develops a business plan for future growth that projects an increase in net income of 0.5 million per year, while the management of Computate develops a plan aimed at increasing its net income by 20% each year.

a. Create standard mathematical model (table, graph, or equations) for the projected net income over time for both companies. Make sure that each model is accurate and labeled properly so that it represents the situation.

b. Compare the two companies. How are the representations of for the net income of the two companies similar? How do they differ? What relationships are highlighted in each representation?

c. If both companies were able to meet their net income growth goals, which company would you choose to invest in? Why?

d. When, if ever, would your projections suggest that the two companies have the same net income? How did you find this? Will they ever have the same net income again?
Can someone help me solve this problem?

Answer 1

The question is an illustration of a linear function and an exponential function.

The given parameters are:

Calculate Company

Initial net income: $8 million

Rate: $0.5 million per year

Computate Company

Initial net income: $3 million

Rate: 20% each year

(a) Standard mathematical model

The model of calculate company is best represented using a linear function, while the computate is best modeled by an exponential function.

A linear function is represented as:

$y = mx + b$

Where:

• m represents rate
• b represents the initial value

An exponential function is represented as:

$y = a(1 + r)^x$

Where:

• r represents rate
• a represents the initial value

So, the functions are:

$y=8 + 0.5x$ --- calculate company

$y =3(1.2)^x$ --- computate company

See attachment for the graph of both functions

(b) Compare both functions

From the graph of both functions, we have the following comparison:

• The calculate company has a higher y-intercept
• The computate company follows a more realistic model

(c) The company to choose

In (b), we concluded that:

The computate company follows a more realistic model

Hence, it is better to invest in the computate company

(d) When both companies have the same net income

From the attached graph, both functions meet at approximately (8, 12)

This means that they have the same net income in 2018

The graphs do not meet again.

This means that, they would never have the same net income again

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