y=
The exponential function is given by
An exponential function is in the form:
Where a is the initial value of y and b is the multiplier factor
Let y represent the population after t years.
Given an initial population of 210000, hence:
The population increases by 12.5% each year, hence:
The exponential function is given by
Find out more on exponential function at: brainly.com/question/12940982
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 kshy15% each year.
a. Create standard mathematical model (table, graph, or equations) for the projected net income for the
next 10 years for both companies. Make sure that each model is accurate and labeled properly so that it
represents the situation
b. If both companies were able to meet their net income growth goals, which company would you choose
to invest in? Why?
c. 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?
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Answer:
a) see the attached spreadsheet (table)
b) Calculate, for a 10-year horizon; Computate for a longer horizon.
c) Year 13; no
Step-by-step explanation:
a) The attached table shows net income projections for the two companies. Calculate's increases by 0.5 million each year; Computate's increases by 15% each year. The result is rounded to the nearest dollar.
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b) After year 4, Computate's net income is increasing by more than 0.5 million per year, so its growth is faster and getting faster yet. However, in the first 10 years, Calculate's net income remains higher than that of Computate. If we presume that some percentage of net income is returned to investors, then Calculate may provide a better return on investment.
The scenario given here is only interested in the first 10 years. However, beyond that time frame (see part C), we find that Computate's income growth far exceeds that of Calculate.
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c) Extending the table through year 13, we see that Computate's net income exceeds Calculate's in that year. It continues to remain higher as long as the model remains valid.
To create a mathematical model for the next 10 years' projected net income for Calculate and Computate, use the given growth rates. Compare the projected net incomes to decide which company to invest in. Find the year when the two companies have the same net income.
To create a mathematical model for the projected net income for the next 10 years for both companies, we can use equations. Let's start with Calculate:
Net Income(Calculate) = 5 + 0.5*year
For Computate, the net income growth rate is 15%, so the equation would be:
Net Income(Computate) = 2 * (1 + 0.15)^year
To compare the two companies' projected net income, we can create a table or graph using the equations. By comparing the values, we can determine which company would be a better choice for investment. To find when the two companies have the same net income, we can set the two equations equal to each other and solve for the year.
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Step-by-step explanation:
Radius:6ft
Diameter:12ft
Area:
circumference:
8 5/12 feet
10 3/7 feet
10 11/12 feet
Answer: 10 11/12 feets
Step-by-step explanation:
The tree has a height of 9 2/3 feet. We will be converting the mixed fraction to improper fraction, it becomes 29/3 feet's. So the tree has a height of 29/3 feets.
The tree grows an additional 1 1/4 feet. We would be converting it from mixed fraction to improper fraction. It becomes 5/4
To determine the new height of the tree, we would add the previous height + the growth in height of the tree. It becomes 29/3 + 5/4 = 131/12
We would convert from improper fraction to mixed fraction. It becomes
10 11/12 feets
∠ABF and ∠CBE are vertical angles
3x + 25 + 7x - 19 = 10x - 6
Set them equal to each other
∠ABF = ∠CBE
6x + 26 = 10x - 6
Isolate the x. Subtract 6x from both sides and add 6 to both sides
6x (-6x) + 26 (+6) = 10x (-6x) - 6 (+6)
26 + 6 = 10x - 6x
Simplify
32 = 4x
Divide 4 from both sides
32/4 = 4x/4
x = 32/4
x = 8
m∠ABF = 6x + 26
Plug in 8 for x
6(8) + 26 = m∠ABF
48 + 26 = m∠ABF
m∠ABF = 74°
74° is your answer for m∠F
hope this helps