Question

5. Find a formula for an exponential function whose graph passes through the points (1,3) and (5,40). 6. Consider the function h(x) = 5/12 - 3x (a) For what values of x is the quadratic function f(x) = 12 - 3x2 zero or positive? (b) What can part (a) tell you about h(x)?

Answer 1

Answer 5:

Data given:

The graph of an exponential function passes through the points (1,3) and (5,40) .

We need to find the formula for the above exponential function.

As we know, the general form of an exponential function is given by -

y = ab

Since the graph of the function passes through the points (1,3) and (5,40), therefore the points should satisfy the general form of the exponential function as -

Point (1,3):

190 = &

. ab = 3 Equation1

Point (5,40):

40 = ab5

:. ab) = 40 Equation 2

On dividing the Equation2 by Equation1, we get -

ab 40

$b^{4}= \frac{40}{3}$

:. b= 1.9109

Now, on substituting the value of "b" in Equation1, we get -

a 1.9109) = 3

. a = 5.7327

is the required exponential function.

:: y = 5.7327(1.9109)