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bearhunter [10]
2 years ago
8

Terrell brought 42 muffins to school for his birthday He gave one each to the 17students in his class and to the 19 student in t

he other third grade class
Mathematics
1 answer:
yan [13]2 years ago
4 0

Answer:

The expression is 42-17-19 OR 42-(17+19).

Step-by-step explanation:

First, we can indicate that we can use subtraction because is giving them away for his birthday.

"He gave one each to the 17 students in his class and to the 19 students in the other third-grade class".

That represents taking away 17 and 19 means that it is subtracting them.

Hope this helps. (:

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Answer:

Part 1) John’s situation is modeled by a linear equation (see the explanation)

Part 2) y=100x+300

Part 3) \$12,300

Part 4) Is a exponential growth function

Part 5) A=6,000(1.07)^{t}  

Part 6) \$11,802.91  

Part 7) Is a exponential growth function

Part 8) A=5,000(e)^{0.10t}    or  A=5,000(1.1052)^{t}  

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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

y=mx+b

The slope is equal to

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The y-intercept or initial value is

b=\$300

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y=100x+300

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John’s situation is modeled by a linear equation

Part 2) Write the model equation for John’s situation

y=100x+300

see part 1)

Part 3) How much money will John have after 10 years?

Remember that

1 year is equal to 12 months

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10 years=10(12)=120 months

For x=120 months

substitute in the linear equation

y=100(120)+300=\$12,300

Part 4) What type of exponential model is Sally’s situation?

we know that    

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

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  

P=\$6,000\\ r=7\%=0.07\\n=1  

substitute in the formula above

A=6,000(1+\frac{0.07}{1})^{1*t}  

A=6,000(1.07)^{t}  

therefore

Is a exponential growth function

Part 5) Write the model equation for Sally’s situation

A=6,000(1.07)^{t}  

see the Part 4)

Part 6) How much money will Sally have after 10 years?

For t=10 years

substitute  the value of t in the exponential growth function

A=6,000(1.07)^{10}=\$11,802.91  

Part 7) What type of exponential model is Natalie’s situation?

we know that

The formula to calculate continuously compounded interest is equal to

A=P(e)^{rt}  

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  

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substitute in the formula above

A=5,000(e)^{0.10t}  

Applying property of exponents

A=5,000(1.1052)^{t}  

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Is a exponential growth function

Part 8) Write the model equation for Natalie’s situation

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see Part 7)

Part 9) How much money will Natalie have after 10 years?

For t=10 years

substitute

A=5,000(e)^{0.10*10}=\$13,591.41

Part 10) 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

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