A new softball dropped onto a hard surface from a height of 25 inches rebounds to about 2/5 the height on each successive bounce. (a) Write a function representing the rebound height for each bounce. (b) Graph the function. (c) After how many bounces would a new softball rebound less than 1 inch?
let f(x) be the height reached after x=0,1,2,3.... f(0) be the original height f(0)=25 in then: f(x)=f(0)(0.40)^x since f(0)=25 f(x)=25(0.40)^x
the number of bounces that it will take for rebound to be less than 1 will be: 25(0.4)^x<1 this can be written as: 0.4^x<0.04 introducing natural logs we get: xln0.4<ln0.04 x(-1.39794)<(-0.39794) x>(-0.39794)/(-1.39794) x>3.513~4
