Question

Write an exponential function y=ab^x for a graph that includes (-4,72) and (-2,18)

Answer 1

Hello,

y=a*b^x
(-4,72)==> 72=a*b^(-4) (1)
(-2,18)==> 18=a*b^(-2) (2)

(1)/(2)==>4=b^(-2)==>b=1/2 or b=(-1/2) to exclude since b>0

b=0.5 and a*0.5²=18==>a=9/2

Y=9/2*0.5^x

Answer 2

Answer:

The exponential function is $y=\frac{9}{2}(\frac{1}{2})^x$.

Step-by-step explanation:

We are given,

The function $y=ab^x$ that passes through the points (-4,72) and (-2,18).

Substituting the values of x and y in the equation gives us,

$72=ab^{-4}$  ................(1)

$18=ab^{-2}$  ..................(2)

Dividing equation (1) by (2), we get,

$\frac{72}{18}=\frac{ab^{-4}}{ab^{-2}}\\\\4=b^{-2}\\\\b^2=\frac{1}{4}\\\\b=\pm \frac{1}{2}$

Since, in exponential function $y=ab^x$, we have b > 0.

Thus, $b=\frac{1}{2}$

Substituting the value in (1) gives us,

$72=a(\frac{1}{2})^{-4}\\\\72=a\times 2^4\\\\72=16a\\\\a=\frac{9}{2}$

Thus, the exponential function is $y=\frac{9}{2}(\frac{1}{2})^x$.