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Given the exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

[tex]\[ y = 530(1.04)^x \][/tex]

Sagot :

GinnyAnswer
Certainly! Let's analyze the given exponential function:

[tex]\[ y = 530(1.04)^x \][/tex]

### Step 1: Identify the Base
In the given exponential function, the base is [tex]\(1.04\)[/tex].

### Step 2: Determine Growth or Decay
- Exponential functions are characterized by the base of the exponent.
- When the base is greater than 1, the function represents growth.
- When the base is less than 1, the function represents decay.

Since the base here is [tex]\(1.04\)[/tex], which is greater than 1, it indicates growth.

### Step 3: Calculate the Percentage Rate of Increase or Decrease
To find the percentage rate:
- Subtract 1 from the base: [tex]\( 1.04 - 1 \)[/tex].
- The result is [tex]\(0.04\)[/tex].
- Convert this decimal to a percentage by multiplying by 100:
[tex]\[ 0.04 \times 100 = 4\% \][/tex]

### Conclusion
- The function represents growth.
- The percentage rate of increase is 4%.

So, the exponential function [tex]\( y = 530(1.04)^x \)[/tex] indicates a growth with a 4% increase rate.
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