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The amount of water vapor, v (in grams), that will saturate 1 kilogram of dry air when the temperature is x degrees Celsius is approximated by the following equation. v=4.04*1.07^(x) For each increase of 1 degree, what is the percent increase in the amount of water vapor required to saturate the air according to this model? (Ignore the % symbol when entering your answer. For example, if the answer is 11.2%, enter 11.2 .)

The amount of water vapor, v v (in grams), that will saturate 11 kilogram of dry air when the temperature is x x degrees Celsius is approximated by the following equation.\newlinev=4.04⋅1.07x v=4.04 \cdot 1.07^{x} \newlineFor each increase of 11 degree, what is the percent increase in the amount of water vapor required to saturate the air according to this model?\newline(Ignore the % \% symbol when entering your answer. For example, if the answer is 11.2% 11.2 \% , enter 1111.22 .)

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Q. The amount of water vapor, v v (in grams), that will saturate 11 kilogram of dry air when the temperature is x x degrees Celsius is approximated by the following equation.\newlinev=4.04⋅1.07x v=4.04 \cdot 1.07^{x} \newlineFor each increase of 11 degree, what is the percent increase in the amount of water vapor required to saturate the air according to this model?\newline(Ignore the % \% symbol when entering your answer. For example, if the answer is 11.2% 11.2 \% , enter 1111.22 .)
  1. Calculate v(x): To find the percent increase, we need to compare the amount of water vapor at a certain temperature xx with the amount at temperature x+1x+1. Let's first calculate the amount of water vapor at temperature xx using the given equation: v(x)=4.04×1.07xv(x) = 4.04 \times 1.07^x
  2. Calculate v(x+1)v(x+1): Now, we calculate the amount of water vapor at temperature x+1x+1:
    v(x+1)=4.04×1.07x+1v(x+1) = 4.04 \times 1.07^{x+1}
    v(x+1)=4.04×1.07x×1.07v(x+1) = 4.04 \times 1.07^x \times 1.07
  3. Find Percent Increase: To find the percent increase, we need to calculate the ratio of the increase to the original amount and then multiply by 100100 to get the percentage.\newlinePercent Increase = [v(x+1)−v(x)v(x)]×100\left[\frac{v(x+1) - v(x)}{v(x)}\right] \times 100
  4. Substitute into Formula: Substitute the expressions for v(x+1)v(x+1) and v(x)v(x) into the percent increase formula:\newlinePercent Increase = [(4.04×1.07x×1.07−4.04×1.07x)(4.04×1.07x)]×100\left[\frac{(4.04 \times 1.07^x \times 1.07 - 4.04 \times 1.07^x)}{(4.04 \times 1.07^x)}\right] \times 100
  5. Simplify Expression: Simplify the expression by factoring out the common terms:\newlinePercent Increase = [(4.04×1.07x×(1.07−1))(4.04×1.07x)]×100[\frac{(4.04 \times 1.07^x \times (1.07 - 1))}{(4.04 \times 1.07^x)}] \times 100
  6. Cancel Common Terms: Cancel out the common terms in the numerator and the denominator: Percent Increase = (1.07−1)×100(1.07 - 1) \times 100
  7. Calculate Percent Increase: Calculate the numerical value for the percent increase:\newlinePercent Increase = (0.07)×100(0.07) \times 100\newlinePercent Increase = 77

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