Question

Suppose the figure shows f(t), the interest rate on an investment t years after the initial deposit. The straight line is tangent to the graph of y=f(t) when t=8. How fast was the internet rate riding at that time?

Answer 1

Concept:

The slope of the tangent to the curve at any point gives the instantaneous rate of change of the function.

From the given graph, it is observed that the line is tangent to the curve at point (8,9).

So the slope of this line will give the rate of change of the function i.e. interest rate at that instant.

The slope (m) of the line joining (0,0) and (8,9) is given by,

$\begin{gathered} m=\frac{9-0}{8-0} \\ m=\frac{9}{8} \\ m=1.125 \end{gathered}$

Since the slope comes out to be positive, it means that the function is increasing with respect to time.

Thus, the interest rate is increasing at the rate 1.125, at the given time instant.