To determine whether the given exponential function [tex]\( y = 990(0.95)^x \)[/tex] represents growth or decay and to find the percentage rate of change, we need to analyze the base of the exponential function, which is 0.95.
1. Identify the base of the exponent:
- In the function [tex]\( y = 990(0.95)^x \)[/tex], the base is 0.95.
2. Determine if it is growth or decay:
- If the base is greater than 1, the function represents exponential growth.
- If the base is less than 1, the function represents exponential decay.
- Since 0.95 is less than 1, the function represents exponential decay.
3. Calculate the percentage rate of change:
- For decay, you can determine the rate of decrease by subtracting the base from 1 and converting the result to a percentage.
- Percentage rate of decrease = [tex]\( (1 - 0.95) \times 100 \)[/tex].
4. Compute the rate:
- [tex]\( 1 - 0.95 = 0.05 \)[/tex].
- Convert 0.05 to a percentage: [tex]\( 0.05 \times 100 = 5 \% \)[/tex].
Therefore, the function [tex]\( y = 990(0.95)^x \)[/tex] represents decay and the percentage rate of decrease is 5%.
Final Answer:
- Growth/Decay: Decay
- Percentage rate: 5% decrease
Growth: □
Decay: ☒ 5% decrease
