Question

Write an exponential equation in the form y = abx whose graph passes through points (−3, 24) and (−2, 12). y = 3x y = 3(0.5)x y = 0.5(3)x y = −3(24)x

Answer 1

Answer:

Option B.

Step-by-step explanation:

The given exponential equation is

$y=ab^x$  ...(1)

It is given that the graph of above equation passes through points (−3, 24) and (−2, 12).

The graph passes through the point (-3,24), so substitute  x=-3 and y=24 in equation (1).

$24=ab^{-3}$   ...(2)

The graph passes through the point (-2,12), so substitute  x=-2 and y=12 in equation (1).

$12=ab^{-2}$   ...(3)

Divide equation (3) by equation (2).

$\dfrac{12}{24}=\dfrac{ab^{-2}}{ab^{-3}}$

$0.5=b$

Substitute b=0.5 in equation (2).

$24=a(0.5)^{-3}$

$24=\dfrac{a}{(0.5)^{3}}$

$24=\dfrac{a}{0.125}$

$24\times 0.125=a$

$3=a$

Substitute a=3 and b=0.5 in equation (1).

$y=3(0.5)^x$

Therefore, the correct option is B.