Question

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Answer 1

Answer:

(a) Brenda saved $23.50.

(b) The rate at which Brenda is saving money is 0.5 dollars per day.

(c) money saved on $J(14)$ is $27.

Step-by-step explanation:

Given:

Initial amount in the jar is, $J(0)=\ 20$

Amount in the jar after a week or 7 days is, $J(7)=\ 23.50$

Brenda is saving money at a linear rate.

(a)

Now, money at the end of the week is the total money saved by Brenda.

Therefore, total money saved by Brenda is equal to the money saved at the end of the week. So,

Total money saved by Brenda = $J(7)=\ 23.50$

(b)

The rate of change of a function is given as:

$Rate=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

Here, $x_1=0,x_2=7, f(x_1)=J(0),f(x_2)=J(7)$

Therefore, the rate at which Brenda saves money is given as:

$Rate=\frac{J(7)-J(0)}{7-0}\\Rate=\frac{23.50-20}{7}\\Rate=\frac{3.5}{7}=0.5\ dollars/day$

Therefore, the rate at which Brenda is saving money is 0.5 dollars per day.

(c)

A linear function is of the form $f(x)=mx+b$, where 'm' is the rate and 'b' is the initial value of the function.

Therefore, the linear function for the money saved by Brenda can be written as:

$J(x)=(Rate)x+J(0)\\J(x)=0.5x+20$

Now, $J(14)$ is given by plugging in 14 for 'x' in the above expression. So,

$J(14)=0.5\times 14+20\\J(14)=7+20=\ 27$

Therefore, money saved on $J(14)$ is $27.