Simplify 2k^8×3k^3
2 answers:
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The question is an illustration of a linear function and an exponential function.
The given parameters are:
<u>Calculate Company</u>
Initial net income: $8 million
Rate: $0.5 million per year
<u>Computate Company</u>
Initial net income: $3 million
Rate: 20% each year
<h3>(a) Standard mathematical model</h3>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:
Where:
- m represents rate
- b represents the initial value
An exponential function is represented as:
Where:
- r represents rate
- a represents the initial value
So, the functions are:
--- calculate company
--- computate company
See attachment for the graph of both functions
<h3>(b) Compare both functions</h3>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
In (b), we concluded that:
The computate company follows a more realistic model
Hence, it is better to invest in the computate company
<h3>(d) When both companies have the same net income</h3>
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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