What is an increasing exponential equation (y=ab^x) thats goes through points (1,18) and (3,648)

Question

Need to write full equation

with graph

Answer 1

Set up your system of equations.

18=a*b^1

648=a*b^3

I would divide the two equations.

648/18 = (ab^3)/(ab)

Simplify.

36 = b^2

b = ±6

(b should be positive for continuous exponential curve)

Plug into the first equation to determine a.

18 = a(6)^1

a = 3

So, the curve is described by y=3*6^x.... or y = 3·(6)^x

The following Python code would draw the curve. I can't seem to embed an image though...

import matplotlib.pyplot as plt

import numpy as np

x = np.arange(0, 3.5, 0.1)

y = 3*6**x

plt.plot(x,y)

plt.plot(1,18,'o')

plt.plot(3,648,'o')

plt.show()

Answer 2

I say a*b¹=18,,,a*b³=648,,,b²=648/18,,,b=6

now a*6=18, a=3