QuestionEstimate the average rate of change of $V(t)$ from $t=2$ to $t=6$ using points $(2,500)$ and $(6,1200)$ . Interpret the result.

Studdy Solution

STEP 1

Assumptions1. The values of $V(t)$ at different points of time $t$ are as follows $(0,400)$ , $(,500)$ , $(4,900)$ , $(6,1200)$ , $(8,1250)$ . . We are asked to estimate the average rate of change of $V(t)$ with respect to $t$ over the interval $[,6]$ .

STEP 2

The average rate of change of a function over an interval $[a,b]$ is given by the difference in the function values at the end points of the interval divided by the difference in the end points of the interval.
$Average\, rate\, of\, change = \frac{V(b) - V(a)}{b - a}$

STEP 3

Now, plug in the given values for $a$ , $b$ , $V(a)$ , and $V(b)$ to calculate the average rate of change.
$Average\, rate\, of\, change = \frac{V(6) - V(2)}{6 -2}$

STEP 4

From the given points, we know that $V(2) =500$ and $V(6) =1200$ .
$Average\, rate\, of\, change = \frac{1200 -500}{6 -2}$

STEP 5

Calculate the average rate of change.
$Average\, rate\, of\, change = \frac{700}{4}$

STEP 6

The average rate of change is175.
The average rate of change of $V(t)$ with respect to $t$ over the interval $[2,6]$ is175. This means that, on average, the value of subprime mortgage debt outstanding in the United States increased by $175 billion per year over the4-year period from$ t=2 $to$ t=6$.

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QuestionEstimate the average rate of change of $V(t)$ from $t=2$ to $t=6$ using points $(2,500)$ and $(6,1200)$ . Interpret the result.

Studdy Solution

STEP 1

Assumptions1. The values of $V(t)$ at different points of time $t$ are as follows $(0,400)$ , $(,500)$ , $(4,900)$ , $(6,1200)$ , $(8,1250)$ . . We are asked to estimate the average rate of change of $V(t)$ with respect to $t$ over the interval $[,6]$ .

STEP 2

The average rate of change of a function over an interval $[a,b]$ is given by the difference in the function values at the end points of the interval divided by the difference in the end points of the interval.
$Average\, rate\, of\, change = \frac{V(b) - V(a)}{b - a}$

STEP 3

Now, plug in the given values for $a$ , $b$ , $V(a)$ , and $V(b)$ to calculate the average rate of change.
$Average\, rate\, of\, change = \frac{V(6) - V(2)}{6 -2}$

STEP 4

From the given points, we know that $V(2) =500$ and $V(6) =1200$ .
$Average\, rate\, of\, change = \frac{1200 -500}{6 -2}$

STEP 5

Calculate the average rate of change.
$Average\, rate\, of\, change = \frac{700}{4}$

STEP 6

The average rate of change is175.
The average rate of change of $V(t)$ with respect to $t$ over the interval $[2,6]$ is175. This means that, on average, the value of subprime mortgage debt outstanding in the United States increased by $175 billion per year over the4-year period from$ t=2 $to$ t=6$.

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QuestionEstimate the average rate of change of V(t)V(t)V(t) from t=2t=2t=2 to t=6t=6t=6 using points (2,500)(2,500)(2,500) and (6,1200)(6,1200)(6,1200). Interpret the result.

Studdy Solution

STEP 1

STEP 2

STEP 3

Now, plug in the given values for aaa, bbb, V(a)V(a)V(a), and V(b)V(b)V(b) to calculate the average rate of change.Average rate of change=V(6)−V(2)6−2Average\, rate\, of\, change = \frac{V(6) - V(2)}{6 -2}Averagerateofchange=6−2V(6)−V(2)​

STEP 4

From the given points, we know that V(2)=500V(2) =500V(2)=500 and V(6)=1200V(6) =1200V(6)=1200.Average rate of change=1200−5006−2Average\, rate\, of\, change = \frac{1200 -500}{6 -2}Averagerateofchange=6−21200−500​

STEP 5

Calculate the average rate of change.Average rate of change=7004Average\, rate\, of\, change = \frac{700}{4}Averagerateofchange=4700​

STEP 6

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QuestionEstimate the average rate of change of $V(t)$ from $t=2$ to $t=6$ using points $(2,500)$ and $(6,1200)$ . Interpret the result.

Now, plug in the given values for $a$ , $b$ , $V(a)$ , and $V(b)$ to calculate the average rate of change.
$Average\, rate\, of\, change = \frac{V(6) - V(2)}{6 -2}$

From the given points, we know that $V(2) =500$ and $V(6) =1200$ .
$Average\, rate\, of\, change = \frac{1200 -500}{6 -2}$

Calculate the average rate of change.
$Average\, rate\, of\, change = \frac{700}{4}$