A new wood stain loses 6.5% of its colour every year in a city that experiences a lot of hot, sunny days.
What percent of colour will a fence in this city have 6 years after being stained?
(1 - .065)^6 * 100%
My Teacher didn't give us an equation that would work with this question, do you guys have any ideas?
Well, let's do the math, shall we? If the wood stain loses 6.5% of its color every year, after 6 years, it would have lost a total of 6 x 6.5% of its color. That calculates to... umm... wait... let me grab a calculator here... *taps on calculator*... Ah! It's 39%! So, after 6 years, the fence in this city would have approximately 39% less color than when it was first stained. That's a lot of sunshine-induced fading! But don't worry, it could add some rustic charm to your fence!
To find the percent of color that a fence will have after 6 years, we need to calculate the remaining color after each year.
Since the wood stain loses 6.5% of its color every year, the remaining color after each year will be 100% - 6.5% = 93.5%.
After the first year, the fence will have 93.5% of its original color.
After the second year, it will have 93.5% * 93.5% = 87.3% of its original color.
After the third year, it will have 87.3% * 93.5% = 81.6% of its original color.
After the fourth year, it will have 81.6% * 93.5% = 76.2% of its original color.
After the fifth year, it will have 76.2% * 93.5% = 71.2% of its original color.
After the sixth year, it will have 71.2% * 93.5% = 66.5% of its original color.
Therefore, the fence will have 66.5% of its color after 6 years.
To find out the percentage of color that a fence will have after 6 years in the city, we need to consider the annual loss of color the wood stain experiences. We know that the wood stain loses 6.5% of its color every year.
To calculate the percentage of color after 6 years, we would subtract the cumulative loss of color from the original color.
Let's assume the original color of the stained fence is 100.
Year 1: The wood stain loses 6.5% of its color, so we subtract 6.5% of 100 from 100.
Color after Year 1 = 100 - (6.5% of 100) = 100 - (0.065 * 100) = 100 - 6.5 = 93.5
Year 2: Since the fence already lost 6.5% of its color in the first year, we need to calculate the color loss only on the remaining color. So, we subtract 6.5% of 93.5 from 93.5.
Color after Year 2 = 93.5 - (6.5% of 93.5) = 93.5 - (0.065 * 93.5) = 93.5 - 6.07875 = 87.42125
Similarly, we can repeat this calculation for each subsequent year until Year 6.
Year 3: Color after Year 2 - (6.5% of color after Year 2)
Year 4: Color after Year 3 - (6.5% of color after Year 3)
Year 5: Color after Year 4 - (6.5% of color after Year 4)
Year 6: Color after Year 5 - (6.5% of color after Year 5)
By repeating these calculations, we will eventually find the color that the fence will have after 6 years.