Question

y = c \cdot a^x that passes through the following points. * XY XY 9. (-1,4) and (1,16) f(x) = 8 \cdot 2^x y = c \cdot a^x y = \frac{a}{4} \cdot a^x \downarrow \downarrow \frac{y}{a^{-1}} = c \cdot \frac{a^x}{a^{-1}} 16 = \frac{a}{4} \cdot a \frac{4}{a^{-1}} = c 16 = \frac{a^2}{4} \frac{a}{y} = c 4 \cdot 16 = a^2 \pm \sqrt{64} = a^2 8 = a 10. (0,3) and (-2, 27) XY XY

          y = c \cdot a^x that passes through the following points.
* 
XY
XY
9. (-1,4) and (1,16)
f(x) = 8 \cdot 2^x
y = c \cdot a^x
y = \frac{a}{4} \cdot a^x
\downarrow
\downarrow
\frac{y}{a^{-1}} = c \cdot \frac{a^x}{a^{-1}}
16 = \frac{a}{4} \cdot a
\frac{4}{a^{-1}} = c
16 = \frac{a^2}{4}
\frac{a}{y} = c
4 \cdot 16 = a^2
\pm \sqrt{64} = a^2
8 = a
10. (0,3) and (-2, 27)
XY
XY

y = c ·a^x that passes through the following points.
*
XY
XY
9. (-1,4) and (1,16)
f(x) = 8 ·2^x
y = c ·a^x
y = (a)/(4) ·a^x
↓↓(y)/(a^-1) = c ·(a^x)/(a^-1)
16 = (a)/(4) ·a
(4)/(a^-1) = c
16 = (a^2)/(4)
(a)/(y) = c
4 ·16 = a^2
±√(64) = a^2
8 = a
10. (0,3) and (-2, 27)
XY
XY

Added by Nicole T.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert James Kiss

09/23/2023

Step 1

Step 1: Given points (-1,4) and (1,16), we can substitute these points into the equation y = c * a^x to form two equations: 4 = c * a^(-1) 16 = c * a Show more…

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Thanks for your feedback!

y = c * a^x that passes through the following points. 9. (-1,4) and (1,16) f(x) = 8 * 2^x flip to y = (a) / (4) * a^x darr 16 = (a) / (4) * a^(') 16 = (a) / (4) * a 4 * 16 = (a^2) / (yx) * (x) / (1) +-√(64) = √(a^2) 8 = a take away. C(4) / (a^(-1)) = c anything to (a) / (n) = c the power of 1 is itself. 10. (0,3) and (-2,27) How do you get 2^x I don't understand what I did wrong y = c * a" that passes through the following points. X Y X Y 9. (-1,4) and (1,16) f(X) = 8 * 2X x y = F 2 = h C L f1ip to take away. the negative anything to the power of 1 is itself. y.16 = a yJ = h9] + B = a 10. (0,3) and (-2,27) x Y X Y