Mathematical Induction Questions and Answers

Flu is spreading exponentially at a school. The number of new flu patients can be modeled using the equation F = 10e0.12d, where d represents the number of days since 10 students had the flu. (a) How many days will it take for the number of new flu patients to equal 50? Determine your answer algebraically using the natural logarithm. Round your answer to the nearest day.

Carly wants to invest $1000 in an account that earns 8% interest, compounded quarterly. How many years will it take for he account to have a value of $5000? Round to the nearest whole number.

Find S, through S, and then use the pattern to make a conjecture about S, Prove the conjectured formula for S, by mathematical induction. Sn:1/22+1/66+1/132+1/220+...+1/11n(n+1) Find S, through S5- (Type an integer or a simplified fraction.) S₁ =

Determine the a) down payment, b) amount of the loan, c) monthly payment, and d) finance charge. Jason Wagner obtains an installment loan to buy a $12,000 Honda Accord. His down payment is 25%, and the APR is 9% for 36 months.

A 75 L gas tank has a leak. After t hours, the remaining volume, V, in litres is V(t) = 75 (1 - t/24) ²,0≤ t ≤ 24. Use the product rule to determine how quickly the gas is leaking from the tank when the tank is 60% full of gas.

-6z² +6z +140/ (z + 5)² (3z-5) Determine the correct partial fraction decomposition for the expression above. Provide your answer below:

You buy fishing equipment costing $268. State taxes are 6.5% and the federal excise tax on this item is 11.45%. What is the total purchase price? (Round your answer to the nearest cent.) $285.42 $296.87 $298.69 $316.11

Use mathematical induction to prove the statement for all positive integers n. 2+14+26+...+(12n-10) = n(6n-4) What is the first step in a mathematical induction proof? A. Show that S₁ is true. B. Show that So is true. C. Show that Sk is true. D. Show that Sk + 1 is true. Show that 2+14+26++ (12n-10) = n(6n-4) for n = 1. Write the statement S₁. 2= (Do not simplify.) Simplify S₁ on the right. 2= Is S₁ a true statement?

A small metal bar, whose initial temperature was 10° C, is dropped into a large container of boiling water. How long will it take the bar to reach 70° C if it is known that its temperature increases 2º during the first second? (The boiling temperature for water is 100° C. Round your answer to one decimal place.) How long will it take the bar to reach 96° C? (Round your answer to one decimal place.)

A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1466 and the standard deviation was 312. The test scores of four students selected at random are 1900, 1190, 2150, and 1350. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The Z-score for 1900 is (Round to two decimal places as needed.) The Z-score for 1190 is (Round to two decimal places as needed.) The z-score for 2150 is. (Round to two decimal places as needed.). The Z-score for 1350 is (Round to two decimal places as needed.). Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The unusual value(s) is/are. (Use a comma to separate answers as needed.) B. None of the values are unusual.

Determine whether the variable is qualitative or quantitative. Explain your reasoning. Medal won in race Is the variable qualitative or quantitative? A. The variable is quantitative because medal won in race is found by measuring or counting. B. The variable is qualitative because medal won in race describes an attribute or characteristic. C. The variable is qualitative because medal won in race is found by measuring or counting. D. The variable is quantitative because medal won in race describes an attribute or characteristic.

Suppose a certain company gave raises of 3% each year for three years followed by raises of 5% for the next two years. a. If an employee has an annual salary of $52,500 after those 5 raises, what was their starting salary? Show a formula or some calculations and explain in words what you are doing. The anual Salary after 5 years = x dollars.1.051.030. b. What was their 'average annual growth' over those 5 years? In other words, if they had the same percentage raise each year, but had the same increase over the 5-year span, what would that constant 1 percentage raise be?

A population numbers 11,000 organisms initially and decreases by 2.9% each year. Suppose P represents population, and t the number of years of growth. Write an exponential model, P, in the form P = a b^t

Suppose you pay $2.00 to roll a fair die with the understanding that you will get back $4.00 for rolling a 2 or a 1, nothing otherwise. What is your expected net winnings? $4.00 -$2.00 -$0.67 $2.00

Compute the area of the region R bounded by the curve r = 1- cosθ. This curve was sketched in the previous homework (and you can refer to that sketch). Use the double integral method (polar integrals; section 14.3), that is, integrate function 1 over the region.

Dan is putting money into a savings account. He starts with $350 in the savings account, and each week he adds $30. Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Dan has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 17 weeks.