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Select the following equations that represent exponential growth. (1 point)

Responses

y=4(13)x
y is equal to 4 times 1 third to the x th power

y=2(2.0)x
y is equal to 2 times 2 point 0 to the x th power

y=3(4.7)x
y is equal to 3 times 4 point 7 to the x th power

y=8(0.2)x
y is equal to 8 times 0 point 2 to the x th power

y=6(1−0.75)x
y is equal to 6 times open paren 1 minus 0 point 7 5 close paren to the x th power

1 answer

Exponential growth occurs when the base of the exponential function is greater than 1. Let's analyze the given equations:

  1. y = 4(13)^x: The base is 13, which is greater than 1. This represents exponential growth.

  2. y = 2(2.0)^x: The base is 2, which is greater than 1. This represents exponential growth.

  3. y = 3(4.7)^x: The base is 4.7, which is greater than 1. This represents exponential growth.

  4. y = 8(0.2)^x: The base is 0.2, which is less than 1. This represents exponential decay, not growth.

  5. y = 6(1−0.75)^x: This simplifies to y = 6(0.25)^x. The base is 0.25, which is less than 1. This also represents exponential decay, not growth.

In summary, the equations that represent exponential growth are:

  • y = 4(13)^x
  • y = 2(2.0)^x
  • y = 3(4.7)^x