Question

A basketball is thrown, and its height above ground is represented by the function f(x)=-3x^2+10x+4. At the same time, a drone takes off from the ground, and its height above ground is represented by the function f(x)=3^x-1. The heights above the ground of the ball and the drone are shown in the graph below.

If x represents time in seconds, approximately how many seconds does it take for the drone to be higher than the basketball?

Answer 1

The drone takes 2.25 seconds to be higher than the basketball.

Explanation:

Based on the definitions given on statement and the image attached below, the red line represents the height of the basketball and the blue line represents the height of the drone, respectively. The height of the drone is higher than the height of the basketball when the y-value of the former is higher than the y-value of the latter. The time is contained in the +x semiaxis.

According to the figure, the drone takes 2.25 seconds to be higher than the basketball.