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(FILL IN THE BLANK)

Analyze the graph of the exponential decay function.

The initial value is _____

The base, or rate of change is _____

The domain is _____

(FILL IN THE BLANK) Analyze the graph of the exponential decay function. The initial-example-1
User Nukesor
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2 Answers

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Initial value = 1
Rate of change = not sure
Domain = (-infinity, infinity)
User Kvark
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The initial value is 1

The base, or rate of change is 1/3

The domain is a set of all real numbers

How to Interpret the Exponential Function Graph?

An exponential function is a function with the general form:

y = abˣ

Where:

a is the initial value ≠ 0

b is the base or rate of change which is a positive real number which is the growth or decay rate

b ≠ 1.

x is the time exponent

In an exponential function, the base b is a constant. The exponent x is the independent variable where the domain is the set of real numbers.

For the graph, we see that:

When x = 0, y = 1. Thus:

a = 1

When x = 1, y = 1/3

When x = 2, y = 1/9

Thus:

b = 1/3

Thus:

The initial value is 1

The base, or rate of change is 1/3

The domain is a set of all real numbers

User Sandeep Joshi
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