Your grandparents have an annuity. the value of the annuity increases each month by an automatic deposit of 1% interest on the previous month's balance. your grandparents withdraw $1000 at the beginning of each month for living expenses. currently, they have $50,000 in the annuity. model the annuity with a dynamical system. will the annuity run out of money? when? hint: what value will an have when the annuity is depleted?

In the 10th grade, i was teamed up in a group of four. our project was on modern history. altho it seemed super hard for many of us. patrick fleming  took charge and showed us the understanding of this project.  his leadership showed great ethics and it taught me, personally, how to others understand, not just to show them, but explain it thoroughly. and altho he was a great teacher i would have changed a few things. one being his attitude. many times he would get frustrated and impatient with the group.  i think  a leader i would have done exactly  what he did but with much more patience and be there more to explain. such as lunch  learning. and giving everybody a chance to try to explain it in their  head.