Mathematics: Give a possible formula for the function below. let a = (-1, 32) and b = (1, 8). (note: use the general exponential function.)

1,073,741,824Step-by-step explanation:...

Give a possible formula for the function below.

joyce945

06.01.2022

Step-by-step explanation:

Let the equation is y = ab^x ............ (1)

Putting the values of point A in equation (1) as follows.

y = ab^x

32 = ab^(-1) ........... (2)

Putting the values of point B in equation (1) as follows.

y = ab^x

8 = ab^(1) ................ (3)

Now, divide the equation (2) by equation (3) as follows.

$\frac{32}{8} = \frac{ab^(-1)}{ab^(1)}$

Cancelling out with common factors, the equation will be written as follows.

4 = $\frac{b^{-1}}{b^1}$

4 = $\frac{1}{b^1 \times b^{1}}$

4 = $\frac{1}{b^2}$

or, $b^{2} = \frac{1}{4}$

Taking square root on both the side, we get

b = ± $\frac{1}{2}$

Case 1. Place the value of b = + $\frac{1}{2}$ in equation (3) as follows.

8 = ab^1

$8 = a(\frac{1}{2})^{1}$

$8 \times 2 = a$

a = 16

Case 2. Place the value of b = - $\frac{1}{2}$ in equation (3) as follows.

8 = ab^1

8 = $a \times (\frac{-1}{2})^{1}$

$- 8 \times 2 = a$

a = - 16

0,0(0 оценок)