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

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 =
`(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`