Subjects algebra

Car Value Decay 52F650

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1. **State the problem:** We have the function $v(t) = 19900(0.84)^t$ which models the value of a car over time $t$ in years. 2. **Find the initial value:** The initial value is the value of the car at $t=0$. $$v(0) = 19900(0.84)^0 = 19900 \times 1 = 19900$$ So, the initial value of the car is 19900. 3. **Determine if the function represents growth or decay:** Since the base of the exponent is $0.84$, which is less than 1, the function represents exponential decay. 4. **Find the percent change each year:** The value changes by a factor of $0.84$ each year. The percent change is calculated as: $$\text{Percent change} = (1 - 0.84) \times 100 = 0.16 \times 100 = 16\%$$ This means the car's value decreases by 16% each year.