Please help me answer all these questions

t 1. You invest $6000 at an annual rate of 4%. Find the balance after 7 years for each type of compounding a) Quarterly b) Monthly c) Continuous 2. In the next problems, complete the table below by finding the balance A when $12,000 is invested at rater for t years, compounded continuously. 10 20 30 40 50 A a) r=4% b) r=6% c) r=6.5% d) r=3.5% 3. Students participating in a psychology experiment attended several lectures on a subject and took an exam. Every month for a year after the exam, the students took a retest to see how much of the material they remembered. The average scores for the group are given by the human memory model f(x)= 75 - 6 Int+1), Osts 12, where t is the time in months. a) What was the average score at the end of t=1 month? b) What was the average score at the end of t=9months? c) What was the average score at the end of t=12 months? 4. The number of bacteria in a culture is increasing according to the law of exponential growth. After 1 hour there are 100 bacteria, and after 2 hours there are 200 bacteria. How many bacteria will there be after 3 hours? 5. Students in a learning theory study took an exam and then retested monthly for 6 months with an equivalent exam. The data obtained in the study are given by the ordered pairs (t, s ), where t is the time (in months) after the initial exam and s is the average score for the class. Use the data to find a logarithmic equations that relates t and s. (1,84.2) (2,78.4) (3,72.1) (4,68.5) (5, 67.1) (6, 65.3) 6. On the day a grandchild is born, a grandparent deposits $2500 in a fund earning 7.5% interest, compounded continuously. Determine the balance in the account on the grandchild's 25th birthday. 7. You have two options of investing $500. The first earns 5% interest compounded annually, and the second earns 7% simple interest. a) Which option do you choose if you want to cash out the investment in 5 years? Why? b) Which option do you choose if you want to cash out the investment in 10 years? Why? c) Which option do you choose if you want to cash out the investment in 20 years? Why? 8. Write a paragraph concerning the difference in simple interest and compound interest and how exponential growth is beneficial if you invest money but not so beneficial if you get a loan