All details are in the picture. Thus, how to do question 6-12? How to set up equations and solve it?

Suppose that the seller, who is 35 years old, decides to sell this basketball at time t, sometime in the next 30 years: 0 g t S 30. At that time t, he will invest the money he gets from the sale in a bank account that earns an intersect rate of r, compounded continuously, which means that after t years, an initial investment of B USD will be mrth Be\" USD. 1When he turns 65, he will take the money in his bank account for his retirement. Let M (t) be the amount of money in his account when he turns 55, where t is the time at which he sells his basketball. o 4. Write down the closed-formed expression of M(t). o 5- Plot your function M(t) against t when A = 980, I9 = 0-5: and r = 0.05. o 6. If those values of the constants were accurate, then when should the seller sell the basket- ball to maximize the amount in his retirement account when he turns 65'? o 7. Plot the function ME} for several different values of 3, while holding r constant. What does a larger value of 6' imply about the value of the basketball over time? (Refer back to question 3.} And now, what does a larger value of 3 imply about the best time to sell the basketball? Do these two facts seem consistent with one another? o 8. Plot the function MU.) for several different values of 1'. while holding 6 constant. What does a larger value of r imply,r about the best time to sell the basketball? Is that consistent with the meaning of r? o 9. Let it; be the optimal time to sell the basketball, i.e., the time that will maximize M [t]. '1"r:,r to nd ta in the general model. Note that your solution should he a function of the constant variables A, 9 and r. o 10. Plot M (t) against t for different combinations of A. I9 and r, and verify that your expres- sion for to does accurately predict when the best time will be to sell the basketball. o 11. Are the properties of to as it relates to 9 and 3" consistent with what you found in step 'i' and step 8