1. **State the problem:** We are given the exponential function $$y = 1100(1.48)^{-7x}$$ and need to determine if it represents growth or decay, and find the percentage rate of increase or decrease per unit of $x$ to the nearest tenth of a percent. 2. **Recall the general form:** An exponential function can be written as $$y = a b^x$$ where: - $a$ is the initial value, - $b$ is the base that determines growth or decay. 3. **Identify growth or decay:** - If $b > 1$, the function represents exponential growth. - If $0 < b < 1$, the function represents exponential decay. 4. **Rewrite the base:** Given $$y = 1100(1.48)^{-7x}$$, rewrite the base as: $$ (1.48)^{-7} = \frac{1}{(1.48)^7} $$ Calculate $(1.48)^7$: $$ (1.48)^7 \approx 1.48^7 = 1.48 \times 1.48 \times 1.48 \times 1.48 \times 1.48 \times 1.48 \times 1.48 \approx 37.59 $$ So, $$ (1.48)^{-7} = \frac{1}{37.59} \approx 0.0266 $$ 5. **Rewrite the function:** $$ y = 1100 (0.0266)^x $$ 6. **Interpretation:** Since the base $0.0266$ is less than 1, the function represents exponential decay. 7. **Calculate the percentage rate of decrease:** The rate of decrease per unit $x$ is: $$ (1 - 0.0266) \times 100\% = 0.9734 \times 100\% = 97.34\% $$ Rounded to the nearest tenth: $$ 97.3\% $$ **Final answer:** The function represents exponential decay with a percentage rate of decrease of approximately **97.3%** per unit of $x$.