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Vlada [557]
3 years ago
13

My son, Garrett, is 11 years old and has a piggy bank that he wants to fill. He started with 5 one dollar bills. Every Saturday

he earns 3 more dollar bills for chores he’s completed. How many one dollar bills will he have by the end of 10 weeks?
1. Write a function model, M(x), that represents the total number of one dollar bills garret will have in one dollar bills, x

2. Identify the independent and dependent quantity.

3. The domain and range are represented as discrete or continuous?

4.What is a reasonable domain and range for this scenario?


Thanks for the help!
Mathematics
1 answer:
Debora [2.8K]3 years ago
8 0

Answer:

1) M(x) = 5 + 3x

2) Dependent variable; 3 dollar bills

Independent variable: chores

3) Range is continuous

Domain is discrete

4) Range: 0 ≤ x ≤ 10

Domain: 5 ≤ M ≤ 35

Step-by-step explanation:

We are told he started with 5 number of $1 dollar bills and that every Saturday, he earns 3 more $1 dollar bill.

Thus, total number of $1 bills earned after x number of Saturdays(weekly) is;

M(x) = 5 + 3x

After 10 weeks, total number is;

M(10) = 5 + 3(10)

M(10) = 35

The dependent variable is the 3 more dollar bills earned each Saturday because it depends on chores he completed. While the independent variable is the chores because it doesn't depend on anything.

After 10 weeks, the range and domain will be;

Range: 0 ≤ x ≤ 10

For the; Domain:

For x = 1, M(0) = 5 + 3(0) = 5

M(10) = 35

Thus;

Domain: 5 ≤ M ≤ 35

The range could be all numbers in the interval from 0 to 10. Thus, it is continuous.

Whereas, the domain doesn't contain all the numbers in the interval from 5 to 35. Thus it is Discrete.

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Answer:

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For this problem we know the following two conditions:

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We can solve for the initial amount A_o and we got:

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Now using the second condition we have this:

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r = \frac{ln(\frac{25}{9})}{15}= 0.06811008317

And replacing this value of r into equation (1) we got:

A_o = \frac{360}{e^{5*0.06811008317}} = 256.0963179

And our exponential model would be:

A(t) = 256.0963179 e^{0.06811008317 t}

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