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Which graph has the largest value for b
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Which graph has the largest value for b ?-example-1
User Roy Ryando
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Answer:

Since graph D is experiencing exponential growth (meaning its b value is greater than 1) and is steeper than graphs E and F (which also experience exponential growth and have b values greater than 1), it has the largest b value.

Explanation:

  • It's clear from the shapes of the 6 graphs that all 6 are exponential functions, whose general form is given by:

y = a(b)^x, where

  • (x, y) is any point on the exponential curve,
  • a is the initial value (value of y when x = 0),
  • and b is the base.

There are two facts we must remember about the base, which determines the shape of the exponential curve:

  • When 0 < b < 1, the graph experiences exponential growth and y decreases as x increases.
  • When b > 1, the graph experiences exponential growth and y increases as x increases.

For curves A, B, and C, y increases as x increases, so we know that the b values of these three curves must be between 0 and 1 (i.e. a decimal).

Thus, they can't have the largest b value out of all the graphs.

For curves D, E, and F, y increases as x increases, so we know that the b values of these three curves must be greater than 1.

Thus, one of these three graphs has the largest b value out of all the graphs.

For any exponential graph with exponential growth (meaning b > 1), a larger b value will result in a steeper curve, meaning that:

  • bigger b values result in the curve being closer to the y-axis, as the curve becomes more vertical/steep;
  • smaller b values result in the curve being closer to the x-axis, as the curve becomes more horizontal/flat.

Since graph D is experiencing exponential growth (meaning its b value is greater than 1) and is steeper than graphs E and F (which also experience exponential growth and have b values greater than 1), it has the largest b value.

User Finrod Felagund
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