Question

Write an exponential function in the form y=ab^x that goes through points (0, 18)and (3, 6174)

Answer 1

Answer:

$y = 18 \times {7}^{x}$

Step-by-step explanation:

Using the formula for exponential function,

$y = ab {}^{x}$

Let plug in 0,18.

$18 = ab {}^{0}$

Using the zero power rule,

$b {}^{0} = 1$

$18 = a \times 1$

$a = 18$

Since a equal 18 let plug in what we know so far

$y = {18b}^{x}$

Now let find b.

Let use the other point, 3,6174

$6174 = {18b}^{3}$

Divide 18 by both sides and we get

$343 = b {}^{3}$

Take the 3rd root of 343

$\sqrt[3]{343} = b = 7$

b=7

The equation is

$y = 18 \times 7 {}^{x}$