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Which of these equations models exponential GROWTH?

y=2(
3
2
​
)
x


y=3(
4
3
​
)
x


y=2(3)
x


y=6(
2
1
​
)
x

1 answer

To determine which of the equations models exponential growth, we need to look at the base of the exponential term.

Exponential growth occurs when the base of the exponent is greater than 1.

Let's analyze each equation:

  1. y = 2( \(\frac{3}{2}\) )^x: Here, the base \(\frac{3}{2}\) is greater than 1. This represents exponential growth.

  2. y = 3( \(\frac{4}{3}\))^x: The base \(\frac{4}{3}\) is also greater than 1. This equation also represents exponential growth.

  3. y = 2(3)^x: The base 3 is greater than 1. This represents exponential growth as well.

  4. y = 6( \(\frac{2}{1}\) )^x: The base \(\frac{2}{1} = 2\), which is greater than 1, so this too represents exponential growth.

In conclusion, all of the following equations model exponential growth:

  • y = 2( \(\frac{3}{2}\) )^x
  • y = 3( \(\frac{4}{3}\) )^x
  • y = 2(3)^x
  • y = 6(2)^x