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tashaunalewis4786
24.09.2019 •
Mathematics
What is the greatest common factor of 5 and 35?
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Ответ:
Part 1) John’s situation is modeled by a linear equation (see the explanation)
Part 2)![y=100x+300](/tpl/images/0520/1827/4a13b.png)
Part 3)![\$12,300](/tpl/images/0520/1827/9ed36.png)
Part 4)![\$2,700](/tpl/images/0520/1827/aa6d0.png)
Part 5) Is a exponential growth function
Part 6)![A=6,000(1.07)^{t}](/tpl/images/0520/1827/79298.png)
Part 7)![\$11,802.91](/tpl/images/0520/1827/810ba.png)
Part 8)![\$6,869.40](/tpl/images/0520/1827/e79cc.png)
Part 9) Is a exponential growth function
Part 10)
or ![A=5,000(1.1052)^{t}](/tpl/images/0520/1827/1697c.png)
Part 11)![\$13,591.41](/tpl/images/0520/1827/d6f1f.png)
Part 12)![\$6,107.01](/tpl/images/0520/1827/e0f75.png)
Part 13) Natalie has the most money after 10 years
Part 14) Sally has the most money after 2 years
Step-by-step explanation:
Part 1) What type of equation models John’s situation?
Let
y ----> the total money saved in a jar
x ---> the time in months
The linear equation in slope intercept form
The slope is equal to
The y-intercept or initial value is
so
therefore
John’s situation is modeled by a linear equation
Part 2) Write the model equation for John’s situation
see part 1)
Part 3) How much money will John have after 10 years?
Remember that
1 year is equal to 12 months
so
For x=120 months
substitute in the linear equation
Part 4) How much money will John have after 2 years?
Remember that
1 year is equal to 12 months
so
For x=24 months
substitute in the linear equation
Part 5) What type of exponential model is Sally’s situation?
we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
therefore
Is a exponential growth function
Part 6) Write the model equation for Sally’s situation
see the Part 5)
Part 7) How much money will Sally have after 10 years?
For t=10 years
substitute the value of t in the exponential growth function
Part 8) How much money will Sally have after 2 years?
For t=2 years
substitute the value of t in the exponential growth function
Part 9) What type of exponential model is Natalie’s situation?
we know that
The formula to calculate continuously compounded interest is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
substitute in the formula above
Applying property of exponents
therefore
Is a exponential growth function
Part 10) Write the model equation for Natalie’s situation
see Part 9)
Part 11) How much money will Natalie have after 10 years?
For t=10 years
substitute
Part 12) How much money will Natalie have after 2 years?
For t=2 years
substitute
Part 13) Who will have the most money after 10 years?
Compare the final investment after 10 years of John, Sally, and Natalie
Natalie has the most money after 10 years
Part 14) Who will have the most money after 2 years?
Compare the final investment after 2 years of John, Sally, and Natalie
Sally has the most money after 2 years