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.

3. solve the system of equations. show your work. y = x^2 - 3x + 4 x + y = 4

1- Let the triangle be ABC, where A is the point of intersection between the shadow and the ground and BC the height of the statue.
The angle of elevation of the sun is equal to the angle CBA (corresponding), so we can write :

tan (50°) = CB (height of statue) / BA (length of shadow)

tan (50°) = CB/30 ==CB = 30 x tan (50°) = 30 x 1.1917 = 35.8 ft 

2 A- P =P₀ (1+i)ⁿ Where P₀ is the initial population, I the rate of growth of the population, P the population after a period of n years and n, the number of tears. (in the problem t = n)
 P = 8500 (1 + 4.5%)ⁿ . This is the requested answer (don't forget n=t)

2 B- When P =70,000
70,000 = 8,500(1+0.045)ⁿ . Divide both sides by 8500
70,000/8,500 = (1+0.045)ⁿ
2.108 = (1.045)ⁿ
ln(2.108) = n. ln(1.045) and n = t = 16.94 ≈ 20 years

3- Your 3rd question is full of error. Rewrite it and I will help you

The answer is 6 weeks