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Which of these equations models exponential GROWTH?

y=6(
2
1
​
)
x


y=3(
4
3
​
)
x


y=2(
3
2
​
)
x


y=2(3)
x

1 answer

To identify which of the equations models exponential growth, we need to analyze the base of the exponential function in each equation. Exponential growth occurs when the base of the exponent is greater than 1.

Here are the equations provided:

  1. \( y = 6\left(\frac{2}{1}\right)^x \) simplifies to \( y = 6(2)^x \) (base = 2, which is > 1; this is exponential growth).

  2. \( y = 3\left(\frac{4}{3}\right)^x \) (base = \(\frac{4}{3}\), which is > 1; this is exponential growth).

  3. \( y = 2\left(\frac{3}{2}\right)^x \) (base = \(\frac{3}{2}\), which is > 1; this is exponential growth).

  4. \( y = 2(3)^x \) (base = 3, which is > 1; this is exponential growth).

All four equations model exponential growth because their bases are greater than 1. However, if you need to choose the ones specifically mentioned, all of them can be classified as modeling exponential growth:

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

Thus, all equations model exponential growth.