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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=65(1.03)^(x)

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. $\newline$ $y=65(1.03)^{x}$

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Write exponential functions: word problems

Full solution

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

\newline

y=65(1.03)^{x}

Determine Growth or Decay: To determine if the function represents growth or decay, we need to look at the base of the exponent, which is $1.03$ in this case. If the base is greater than $1$ , the function represents growth. If the base is less than $1$ , the function represents decay.
Function Represents Growth: Since $1.03$ is greater than $1$ , the function $y=65(1.03)^{x}$ represents exponential growth.
Calculate Percentage Rate: To find the percentage rate of increase, we subtract $1$ from the base of the exponent and then convert it to a percentage. The base of the exponent is $1.03$ , so we calculate $1.03 - 1 = 0.03$ .
Convert to Percentage: To convert $0.03$ to a percentage, we multiply by $100$ . So, $0.03 \times 100 = 3\%$ .

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