1. While exploring the wild meadows and forests nearby, Jada has found many strange beings. To Jada, the strangest and most concerning beings are the carnivorous weeds. When Jada first noticed the weeds, there were only a few of them, but together, they managed to eat an entire rabbit. In further explorations, Jada found that the weeds reproduced slowly at first, but now, they reproduce rather quickly. Four days after Jada first noticed the weeds, there were only 10, but one week later, there were already 25 weeds.

(a) Using the information above, Jada makes two functions, L(d) and E(d).

L(d) is the number of weeds d days after Jada first noticed them if the weeds reproduce at a linear pace.

E(d) is the number of weeds d days after Jada first noticed them if the weeds reproduce at an exponential pace.

Find formulas for both L(d) and E(d).

(b) Jada decides that E(d) is a more accurate model to use than L(d). Why does this make

sense in the given context?

(c) Using E(d), find the number of carnivorous weeds that ate the rabbit when Jada first

noticed them. Give your answer in exact form and rounded to the nearest whole number.

(d) Under the exponential model E(d), find the growth factor, growth rate (as a percentage), and continuous growth rate. Give your answers in exact form and rounded to the nearest two decimal places.

(e) Jada notices that because E(d) is an increasing exponential function, there are restric- tions on what the growth factor, growth rate, and continuous growth rate may be. If an exponential function is increasing, what must be true about each of these values? Why?

(f) How long does it take for the number of weeds to triple? Be sure to show all of your work.