Question

problem 17
31 the table below shows the radioactivity level of a substance after the given time, t, in seconds.

time (seconds)	radioactivity level
1	10
2	5
3	2.5
4	1.25

what is the average rate of change in radioactivity level over the interval (1 leq t leq 3)?

1. 3.75
2. -3.75
3. 4.6875
4. -4.6875

f.le.b.5: modeling linear functions (linear equations)
problem 18
33 the amount of money a plumber charges is represented by the function (p(h) = 45 + 90h). the best interpretation of the y - intercept of this function is that the plumber charges

1. $45 to come to the house
2. $45 per hour that he works
3. $90 to come to the house
4. $90 per hour that he works

Explanation:

Problem 17

Step1: Recall average rate formula

The average rate of change of a function $f(t)$ over $a \leq t \leq b$ is $\frac{f(b)-f(a)}{b-a}$.

Step2: Identify values from table

For $t=1$, $f(1)=10$; for $t=3$, $f(3)=2.5$.

Step3: Substitute into formula

$\frac{2.5 - 10}{3 - 1} = \frac{-7.5}{2}$

Step4: Calculate the result

$\frac{-7.5}{2} = -3.75$

The function $p(h)=45+90h$ follows the linear form $y=mx+b$, where $b$ (the y-intercept) is the constant value when $h=0$ (0 hours worked). This represents a fixed, one-time charge before any hourly work begins.

Answer:

1. $-3.75$

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Problem 18