MATHEMATICS MIDDLE SCHOOL

John, Sally, and Natalie would all like to save some money. John decides that itwould be best to save money in a jar in his closet every single month. He decides
to start with $300, and then save $100 each month. Sally has $6000 and decides
to put her money in the bank in an account that has a 7% interest rate that is
compounded annually. Natalie has $5000 and decides to put her money in the
bank in an account that has a 10% interest rate that is compounded continuously.

How much money have after 2 years?

How much money will sally have in 10 years?

What type of exponential model is Natalie’s situation?

Write the model equation for Natalie’s situation

How much money will Natalie have after 2 years?

How much money will Natalie have after 10 years

Answers

Answer 1

Answer:

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) $\$2,700$

Part 5) Is a exponential growth function

Part 6) $A=6,000(1.07)^(t)$

Part 7) $\$11,802.91$

Part 8) $\$6,869.40$

Part 9) Is a exponential growth function

Part 10) $A=5,000(e)^(0.10t)$ or $A=5,000(1.1052)^(t)$

Part 11) $\$13,591.41$

Part 12) $\$6,107.01$

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

y=mx+b

The slope is equal to

$m=\$100\ per\ month$

The y-intercept or initial value is

$b=\$300$

$y=100x+300$

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

$10\ years=10(12)=120 months$

For x=120 months

substitute in the linear equation

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

Part 4) How much money will John have after 2 years?

Remember that

1 year is equal to 12 months

$2\ years=2(12)=24\ months$

For x=24 months

substitute in the linear equation

$y=100(24)+300=\$2,700$

Part 5) What type of exponential model is Sally’s situation?

we know that

The compound interest formula is equal to

$A=P(1+(r)/(n))^(nt)$

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

$P=\$6,000\n r=7\%=0.07\nn=1$

substitute in the formula above

$A=6,000(1+(0.07)/(1))^(1*t)\n A=6,000(1.07)^(t)$

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

$A=6,000(1.07)^(10)=\$11,802.91$

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

$A=6,000(1.07)^(2)=\$6,869.40$

Part 9) 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

$P=\$5,000\nr=10\%=0.10$

substitute in the formula above

$A=5,000(e)^(0.10t)$

Applying property of exponents

$A=5,000(1.1052)^(t)$

therefore

Is a exponential growth function

Part 10) Write the model equation for Natalie’s situation

$A=5,000(e)^(0.10t)$ or $A=5,000(1.1052)^(t)$

see Part 9)

Part 11) 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 12) How much money will Natalie have after 2 years?

For t=2 years

substitute

$A=5,000(e)^(0.10*2)=\$6,107.01$

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

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Answers

The slop is up 1, over 3, so that eliminates A and B, then the intercept is -2 so that means the answer is D

your answer is (D) because, for the equation y=1/3x-2, look for -2 on the y-axis and then see what way the line is going. If it is going left down to right up or the other way. If it is left down to right up then it is a positive slope. The slope is 1/3 obviously positive. so use the rule for slope rise over run (rise/run) which means the number on the top you go up if it is positive and down if it I negative. And with the one on the bottom, you go right that many spaces depending on what the number is. So you will go to -2 on y-axis and go up 1 time and go to the right 3 times. Srry it is so much I am just trying to explain it the best I can so you understand how I got that answer. :)

isaiash puts a 10 gram weight on a pan balance. how many 1gram weights does he need to balance the scale?

Answers

He would need to put 10 cause 1 gram per weight to equal 10 you would need 10 1 gram weights.

What is the quotient of 12,228 divided by 24

Answers

Answer:

509.5

Step-by-step explanation:

98 is 35% of what number

Answers

'is' in mathematics means equal
'of' in mathematics means multiplication

35% can also be written as 35/100

$98 = (35)/(100) * x\n\n98 * (100)/(35) = x\n\n x = (9800)/(35)\n\nx = \boxed{\bf{280}}$

Answer:

The number is 280

Explanation:

Assume that the number we are looking for is x

We are given that:

35% of the number is 98

This means that:

35% * x = 98

0.35x = 98

x = $(98)/(0.35)$