Solve Systems Approximately Worksheets Grade 9

1. Sophia is studying the population of a rare bird species on an island. The bird population (in hundreds) after t years is modeled by the exponential function B(t) = 6 * (1.1)^t. The available food supply (in thousands of kilograms) is modeled by the linear function F(t) = 21 - t. Using graphing technology, find approximately how many years it will take for the bird population to reach 1,200 birds while the food supply is still above 16 thousand kilograms.
2. Use technology to solve the system: y = x³ - 7x + 3 and y = 3ˣ - 5. Find the approximate intersection point where x is positive and odd.
3. A rocket's height h (in meters) is modeled by the quadratic function h(t) = -5t² + 80t + 20, where t is time in seconds after launch. Using technology, find the time when the rocket reaches its maximum height. Round your answer to the nearest tenth of a second.

…and 5 more problems

1. Emma is monitoring the height of a rocket launched from a platform. The rocket's height (in meters) above the ground is modeled by the quadratic function h(t) = -5t² + 40t + 10, where t is time in seconds after launch. A nearby drone's height is modeled by the linear function d(t) = 10t + 25. Using graphing technology, determine approximately how many seconds after launch the rocket and the drone are at the same height. Round your answer to the nearest tenth of a second.
2. Use technology to solve the system: y = x³ - 7x² + 14x - 8 and y = 3ˣ - 9. Find the approximate intersection point where x > 4.
3. Emma is analyzing the profit function for her small business. The profit P(x) in dollars from selling x units of her product is modeled by the quadratic equation P(x) = -2x² + 120x - 1000. Using graphing technology, determine approximately how many units Emma needs to sell to break even (where profit equals zero). Round your answer to the nearest whole number.

…and 4 more problems

1. Liam is designing a rectangular garden with a perimeter of 40 meters. He wants the length to be 4 meters more than the width. Write a system of equations to represent this situation and solve it to find the dimensions of the garden.
2. A right triangle is drawn on a coordinate plane with vertices at (0,0), (6,0), and (6,8). A circle is inscribed within this triangle such that it touches all three sides. What is the area of this inscribed circle? (Use π = 3.14)
3. Emma uses a graphing calculator to solve the system of equations: y = 3^x and y = 7x - 3. What is the approximate x-coordinate of the point where the two graphs intersect? (Round your answer to three decimal places.)

…and 4 more problems