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# 1. A statue creates a shadow that is 30 ft long. The angle of elevation of the sun is 50.

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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.

Jun 6, 2018

#1
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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.

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 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 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.

Jun 6, 2018

#1
+2422
+1

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.

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 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 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.

TheXSquaredFactor Jun 6, 2018
#2
+964
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I substituded into the formula, but I'm not sure if its correct. :(

AngelRay  Jun 7, 2018