Answer:
62.54 meters
Step-by-step explanation:
If we let the initial level of water in the dam as Li meters and the final water level as Lf meters and if the rate of decrease of the level is r% per year then the final level after t years can be computed from the formula
[tex]L_f = L_i(1- r)^t[/tex] [1]
where r = rate of decrease as a decimal
GIven:
Plugging these values into the formula [1]
Final Level
[tex]L_f= 270(1-0.15)^9[/tex]
[tex]L_f= 270(0.85)^9[/tex]
[tex]L_f = 62.54 \;meters[/tex]
The water level in the dam after 9 years will be approximately 99.26 meters, calculated by the formula for exponential decay and rounding to the nearest hundredth.
To calculate the water level in a dam after it decreases by 15% each year for 9 years, we use the formula for exponential decay: final amount = initial amount × (1 - rate of decay)number of years. In this case, the initial amount is 270 meters, the rate of decay is 0.15, and the number of years is 9.
First, we calculate the factor by which the water level decreases each year: 1 - 0.15 = 0.85. Then we raise this factor to the power of 9 to find the decay factor over 9 years: 0.859.
Next, we multiply the initial water level by the decay factor: 270 × 0.859. Using a calculator, this comes out to approximately 99.26 meters. Therefore, the water level in the dam will be around 99.26 meters after 9 years.
The final step is to round the answer to the nearest hundredth, so the final water level is 99.26 meters.