Question

# Let f$t$ = 1/t. Find a value of t such that the average rate of change of f$t$ from 1 to t equals -1/13.

142

likes
712 views

## Answer to a math question Let f$t$ = 1/t. Find a value of t such that the average rate of change of f$t$ from 1 to t equals -1/13.

Fred
4.4
Solution:
1. The average rate of change of a function f$t$ from t = a to t = b is given by:
\frac{f$b$ - f$a$}{b - a}

2. Given:
* Function: f$t$ = \frac{1}{t}
* Interval: [1, t]
* Average rate of change: -\frac{1}{13}

3. Substitute the given values into the formula:
\frac{f$t$ - f$1$}{t - 1} = -\frac{1}{13}

4. Evaluate f$1$:
f$1$ = \frac{1}{1} = 1

5. Substitute f$1$ and f$t$:
\frac{\frac{1}{t} - 1}{t - 1} = -\frac{1}{13}

6. Simplify the numerator:
\frac{1 - t}{t$t - 1$} = -\frac{1}{13}

7. Multiply both sides by t$t - 1$:
1 - t = -\frac{t$t - 1$}{13}

8. Distribute and simplify:
1 - t = -\frac{t^2 - t}{13}
13$1 - t$ = -t^2 + t
13 - 13t = -t^2 + t

9. Rearrange into a standard quadratic equation:
t^2 - 14t + 13 = 0

$t - 13$$t - 1$ = 0

11. Solve for t:
Frequently asked questions $FAQs$