Unit 6, Lesson 6
Analyzing Graphs
Algebra 1
Practice
Problem 1
The two graphs show models characterized by exponential decay representing the area covered by two different algae blooms, in square yards, \(w\) weeks after different chemicals were applied.
- Which algae bloom covered a larger area when the chemicals were applied? Explain how you know.
- Which algae population is decreasing more rapidly? Explain how you know.
Graph of two functions on grid, origin O. Horizontal axis, time in weeks, from 0 to 6 by 1's. Vertical axis, area covered, from 0 to 600 by 50's.
Approximate Plotted coordinates as follows: For red triangles: 0 comma 500, 1 comma 330, 2 comma 225, 3 comma 150, 4 comma 100, 5 comma 65, 6 comma 40. For blue dots: 0 comma 200, 1 comma 160, 2 comma 125, 3 comma 100, 4 comma 80, 5 comma 65, 6 comma 50.
Problem 2
A medicine is applied to a burn on a patient's arm. The area of the burn in square centimeters decreases exponentially and is shown in the graph.
- What fraction of the burn area remains each week?
- Write an equation representing the area of the burn, \(a\), after \(t\) weeks.
- What is the area of the burn after 7 weeks? Round to three decimal places.
Graph of a function on grid, origin O. Horizontal axis, time in weeks, from 0 to 6 by 1's. Vertical axis, area in square centimeters, from 0 to 9 by 1's. Plotted coordinates as follows:
0 comma 8, 1 comma 6, 2 comma 4 point 5, 3 comma 3 point 375, 4 comma 2 point 5, 5 comma 1 point 9.