11 A ball is dropped from a height of 10 feet. The ball repeatedly bounces, and the maximum height of the ball after each bounce is \( 20 \% \) less than the previous maximum height. Which of the following arguments is correct regarding a sequence that can be used to model the successive maximum heights, in feet?

Evaluate or simplify the expression without using a calculator. \( e^{\ln 3 x^{3}} \) \( e^{\ln 3 x^{3}}=\square \)

2) \( f(x)=\frac{x^{2}+x}{3 x^{2}-12} \)

Given two points for an exponential function, 1. Use the two points to find the growth rate, k . Write an exponential model for each point, then solve this system of two equations for k . 2. Use either point with the k you found to find the initial amount at time zero, \( \mathrm{A}_{\mathrm{o}} \). 3. Doubling time is when the amount is \( 2^{*} \mathrm{~A}_{\mathrm{o}} \). 4. Use the values of k and \( \mathrm{A}_{\mathrm{o}} \) to calculate the amount for a given time or to find the time to reach a specific amount in the future. The count in a bacteria culture was 600 after 20 minutes and 1900 after 30 minutes. Assuming the count grows exponentially. You may enter the exact value or round to 2 decimal places. What was the initial size of the culture? Find the doubling period. Find the population after 105 minutes. When will the population reach 14000 .

A wooden artifact from an ancient tomb contains 40 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.) years

Graph \( m(w)=-2 \cdot 2^{w} \)