State the growth factor in each of the following situations.
Newspaper readership is declining by 7 1/3 % per year.
A bouncing ball rebounds to 1/3 of its previous height.
Dont know how to solve these fractions:\ I just hate working with fractions.
If readership declines 7 1/3% each year, then the readership in year n+1 r(n+1) = (1-.0733333)*r(n) = 0.926666 r(n)
So, the growth factor r = 0.926666 (or 139/150)
Similarly, for the ball, height h(n+1) = 1/3 h(n) so the growth factor is 1/3.
To determine the growth factor in each situation, we need to understand how to calculate a growth factor. A growth factor represents how much a quantity is increasing (greater than 1) or decreasing (between 0 and 1).
In the first situation, the newspaper readership is declining by 7 1/3% per year. To find the growth factor, we need to calculate the percentage decrease and convert it into a decimal value.
Step 1: Convert the fraction 7 1/3 to a decimal. Divide 1 by 3 and add the result to 7.
7 + (1 ÷ 3) = 7 + (0.33) = 7.33
Step 2: Convert 7.33% into a decimal by dividing it by 100.
7.33 ÷ 100 = 0.0733
Step 3: Calculate the growth factor by subtracting the decimal value from 1.
1 - 0.0733 = 0.9267
Therefore, the growth factor in this situation is approximately 0.9267, indicating a decline of 7 1/3% per year.
In the second situation, a bouncing ball rebounds to 1/3 of its previous height. Here, we want to find the growth factor representing the decrease in height.
Step 1: Convert 1/3 into a decimal by dividing the numerator by the denominator.
1 ÷ 3 = 0.3333 (rounded to four decimal places)
Step 2: Calculate the growth factor by subtracting the decimal value from 1.
1 - 0.3333 = 0.6667
Therefore, the growth factor in this situation is approximately 0.6667, indicating that the ball rebounds to 2/3 of its previous height.
Regarding your difficulty with fractions, I understand that working with fractions can sometimes be challenging. Here are some general guidelines to help solve fractions:
1. Addition and Subtraction: Make sure the denominators are the same. If not, find a common denominator by multiplying both denominators together.
2. Multiplication: Multiply the numerators together and the denominators together. Simplify the resulting fraction if possible.
3. Division: Invert (flip) the second fraction and multiply it by the first fraction. Simplify as needed.
4. Converting to decimals: Divide the numerator by the denominator.
There are also online calculators and software programs available that can help with fraction calculations if you find them challenging. Practice and familiarity with fractions will make them easier to work with over time.