Please Solve Using Python Programming

In Exercises 19 through 31, write a program to answer the question.

19. AgeA person born in 1980 can claim, I will be x years old in the year x squared. What is the value of x? See Fig. 3.31.

Person will be 45 in the year 2025. FIGURE 3.31 Outcome of Exercise 19.

21. Radioactive DecayStrontium-90, a radioactive element that is part of the fallout from nuclear explosions, has a half-life of 28 years. This means that a given quantity of strontium-90 will emit radioactive particles and decay to one-half its size every 28 years. How many years are required for 100 grams of strontium-90 to decay to less than 1 gram? See Fig. 3.33.

The decay time is 196 years.

FIGURE 3.33 Outcome of Exercise 21.

23. Car LoanWhen you borrow money to buy a house or a car, the loan is paid off with a sequence of equal monthly payments with a stated annual interest rate compounded monthly. The amount borrowed is called the principal. If the annual interest rate is 6% (or .06), then the monthly interest rate is .06/12=.005..06/12=.005. At any time, the balance of the loan is the amount still owed. The balance at the end of each month is calculated as the balance at the end of the previous month, plus the interest due on that balance, and minus the monthly payment. For instance, with an annual interest rate of 6%,

[new balance]=[previous balance]+.005[previous balance][monthly payment] =1.005[previous balance][monthly payment]. [new balance]=[previous balance]+.005[previous balance][monthly payment] =1.005[previous balance][monthly payment].

Suppose you borrow $15,000 to buy a new car at 6% interest compounded monthly and your monthly payment is $290.00. After how many months will the car be half paid off? That is, after how many months will the balance be less than half the amount borrowed? See Fig. 3.35 on the next page.

Loan will be half paid off after 33 months.

FIGURE 3.35 Outcome of Exercise 23.

25. AnnuityAn annuity is a sequence of equal periodic payments. For one type of annuity, a large amount of money is deposited into a bank account and then a fixed amount is withdrawn each month. Suppose you deposit $10,000 into such an account paying 3.6% interest compounded monthly, and then withdraw $600 at the end of each month. The monthly interest rate will be .036/12 or .003, and the balance in the account at the end of each month will be computed as

[balance at end of month]=(1.003)[balance at end of previous month]600.[balance at end of month]=(1.003)[balance at end of previous month]600.

After how many months will the account contain less than $600, and what will be the amount in the account at that time? See Fig. 3.37.

Balance will be $73.91 after 17 months.

FIGURE 3.37 Outcome of Exercise 25.

27. Same Birthday as YouSuppose you are in a large-lecture class with n other students. Determine how large n must be such that the probability that someone has the same birthday as you is greater than 50%? See Fig. 3.39. Note: Forgetting about leap years and so assuming 365 days in a year, the probability that no one has the same birthday as you is (364365)n.(364365)n.

With 253 students, the probability is greater than 50% that someone has the same birthday as you.

FIGURE 3.39 Outcome of Exercise 27.

29. Population GrowthIn 2014 Chinas population was about 1.37 billion and growing at the rate of .51% per year. In 2014 Indias population was about 1.26 billion and growing at the rate of 1.35% per year. Determine when Indias population will surpass Chinas population. Assume that the 2014 growth rates will continue. See Fig. 3.41.

India's population will exceed China's population in the year 2025.

FIGURE 3.41 Outcome of Exercise 29.

31. Saving AccountWrite a menu-driven program that allows the user to make transactions to a savings account. Assume that the account initially has a balance of $1,000. See Fig. 3.43.

Options: 1. Make a Deposit 2. Make a Withdrawal 3. Obtain Balance 4. Quit Make a selection from the options menu: 1 Enter amount of deposit: 500 Deposit Processed. Make a selection from the options menu: 2 Enter amount of withdrawal: 2000 Denied. Maximum withdrawal is $1,500.00 Enter amount of withdrawal: 600 Withdrawal Processed. Make a selection from the options menu: 3 Balance: $900.00 Make a selection from the options menu: 4

FIGURE 3.43 Possible outcome of Exercise 31.