Question

For problems a - d, write the function in the form LaTeX: y=ab^x. y = a b x . a) LaTeX: y=3\sqrt{4^{2x}} y = 3 4 2 x b) LaTeX: y=\frac{\sqrt[3]{5^{3x}}}{2} y = 5 3 x 3 2 c) LaTeX: y=8^{x+2} y = 8 x + 2 d) LaTeX: y=\frac{3^{2x+1}}{\sqrt{3^{2x}}}

Answer 1

Step-by-step explanation:

To write the equation in LaTeX in form y = ab^x  or $ab^x$ for y = abx .........(1)

(a) LaTeX: y=3\sqrt{4^{2x}}  y = 3 4 2 x can be written in mathematical form as

$y=3\sqrt{4^{2x}}$ ; y = 342x

on comparing with equation (1) we get a =3 and b =4

⇒y = 34^x or $34^x$

(b) LaTeX: y=\frac{\sqrt[3]{5^{3x}}}{2} y = 5 3 x 3 2 can be written in mathematical form as

$y=\frac{\sqrt[3]{5^{3x}}}{2}$ ; y = 342x

on comparing with equation (1) we get a =0.5 and b =5

⇒y = $\frac{1}{2}5^x$

(c)LaTeX: y=8^{x+2} y = 8 x + 2 can be written in mathematical form as

$y=8^{x+2}$

on comparing with equation (1) we get a =64 and b =8

y = $64 . 8^x$

(d)LaTeX: y=\frac{3^{2x+1}}{\sqrt{3^{2x}}}  can be written in mathematical form as

$y=\frac{3^{2x+1}}{\sqrt{3^{2x}}}$ = $3^{x+1}$ = $3 . 3^x$

on comparing with equation (1) we get a =3 and b =3

y = $3 . 3^x$