Question

Write an exponential function to describe the given sequence of numbers, assuming that the first number in the sequence corresponds to x = 0.
5.30, 180, 1080, 6480...

Answer 1

Answer:

$y = 5(6) {}^{x}$

Step-by-step explanation:

A exponential function is represented by

$y = ab {}^{x}$

where a is the vertical stretch and b is the base and x is the nth

power of x

Since the first number corresponds with zero, that means our y intercept is the first number.

This means when x=0 , y=5 so let find the value of 5.

$5 = ab {}^{0}$

b to the 0th power equal 1 so

$5 = a \times 1$

$a = 5$

Our equation is for now

$y = 5b {}^{x}$

Now let plug in 1,30

$30 = 5b {}^{1}$

Divide 5 by both sides

$6 = b {}^{1}$

Anything to the 1st power is itself so b equal 6.

So our equation is

$y = 5(6) {}^{x}$