Question

Write an exponential equation in the form y = abx whose graph passes through points (4, 8) and (6, 32).

Answer 1

Answer:

Option C.

Step-by-step explanation:

The general exponential equation is

$y=ab^x$

It is given that the graph of exponential function passes through points (4,8) and (6,32). It means the equation of exponential function must be satisfied by these points.

$8=ab^4$       ...(1)

$32=ab^6$       ...(2)

Divide equation (2) by equation (1).

$\dfrac{32}{8}=\dfrac{ab^6}{ab^4}$

$4=b^2$

Taking square root on both sides.

$2=b$

Put b=2 in (1).

$8=a(2)^4$

$8=16a$

$\dfrac{8}{16}=a$

$0.5=a$

Substitute a=0.5 and b=2 in the given general exponential equation.

$y=0.5(2)^x$

Therefore, the correct option is C.