QuestionMath 19 Models and Word Problems Worksheet
1. A surveyor plants a stake on one side of a road that runs east to west. The surveyor then walks directly across the road, walks 5 meters to the east, and plants a second stake. The distance between the two stakes is 13 meters. If the surveyor continues to walk to the east a further 11 meters, what would the distance between the surveyor and the first stake be? (a) Begin by drawing a picture, labeling the position of all stakes and distances, including unknowns. Which variable are you solving for? Will there be any intermediate variables you will need to solve for before finding the final answer? (b) Use the Pythagorean Theorem to find the width of the road in meters. (c) Using the information you have, apply the Pythagorean Theorem to solve the original problem.
2. I own a ladder that is 20 feet tall and lean it up against a wall at an angle. The distance between the top of the ladder and the ground is triple the distance between the base of the wall and the bottom of the ladder. What is the distance between the bottom of the ladder and the base of the wall? (Round your answer to the nearest tenth of a foot.)
3. Bamboo is one of the fastest growing plants in the world. Suppose I plant some 15 inch bamboo in my garden. Assume for all parts of this problem that bamboo grows at 35 inches per day. (Amazingly, this is a low estimate for its growth rate!) (a) Write a linear model/function for the height of $h(t)$ the bamboo as it relates to time $t$ in days where $t=0$ is the day I planted it. (b) Express the height of the bamboo on the day that it was planted (c) I have a fence at the back of my garden that is 10 ft tall. How long will it be from the planting of the bamboo until it is as tall as my fence? (d) If we instead choose $t=0$ to be the day that the bamboo is the same height as the fence, how will the model change? (e) How would the model change if we expressed the time $t$ in weeks instead of days?
4. The University of Golden Bears has been working on increasing its enrollment numbers since the year 2005. In 2010, the student population was 11,000 students and by 2020 , the student population was 14,000. (a) Write a function of time $t$ representing the population $P$. Assume the growth of the student population was linear and use $t=0$ at 2005. (b) What would the model be instead if $t=0$ at 2010?