1. A statue creates a shadow that is 30 ft long. The angle of elevation of the sun is 50°.
(a) Draw a diagram that represents this situation.
(b) How tall is the statue? Round your answer to the nearest tenth of a foot. Show your work.
2. In 2010, the population of a town is 8500. The population decreases by 4.5% each year.
(a) Write an equation to find the population of the town t years after 2010.
(b) In what year will the population of the town be 7000? Show your work.
1) It turns out that someone has already asked this question already, and I just happen to remember this post from February 27 of this year. I see no reason to make a duplicate answer.
Here is the link: https://web2.0calc.com/questions/help_80894
2a) The following equation below shows the general formula for a function that has exponential growth or decay.
\(P(t)=a*b^t\)
\(P(t)\) represents the function that yields the population of the town t years after 2010.
a = initial population of town
b = rate of exponential growth or decay
Since a is the initial population of the town, a=8500.
b, in this case, represents the portion of the population that remains as a fraction or decimal. The population begins at 100%. If the population decreases by 4.5% every year, then 100%-4.5% or 95.5% represents the percentage of the population that remains. As a decimal, this would be written as 0.955.
Now that both of this function are known, we can create an equation to find the population t years after 2010.
\(P(t)=8500(0.955)^t\)
2b) Since I have generated the equation for you, do you think that you could solve the next one? Just substitute into the formula and solve.
1) It turns out that someone has already asked this question already, and I just happen to remember this post from February 27 of this year. I see no reason to make a duplicate answer.
Here is the link: https://web2.0calc.com/questions/help_80894
2a) The following equation below shows the general formula for a function that has exponential growth or decay.
\(P(t)=a*b^t\)
\(P(t)\) represents the function that yields the population of the town t years after 2010.
a = initial population of town
b = rate of exponential growth or decay
Since a is the initial population of the town, a=8500.
b, in this case, represents the portion of the population that remains as a fraction or decimal. The population begins at 100%. If the population decreases by 4.5% every year, then 100%-4.5% or 95.5% represents the percentage of the population that remains. As a decimal, this would be written as 0.955.
Now that both of this function are known, we can create an equation to find the population t years after 2010.
\(P(t)=8500(0.955)^t\)
2b) Since I have generated the equation for you, do you think that you could solve the next one? Just substitute into the formula and solve.