Exam 5: Growth and Decay: An Introduction to Exponential Functions

Write a function in the form for an exponential function where and .

The half-life of penicillin in a beef cow is approximately 30 hours. If a beef cow is administered 45 mL of penicillin, how long will it take for the animal to reach the acceptable level for butchering of 0.5 mL? (Round your answer to the nearest tenth of an hour.)

The population of the world increased from 5.61 billion in 1995 to 6.03 billion in 2000. Assuming this (exponential) growth continues, to the nearest year how many years will it take for the world's population to double?

Find an exponential function, , such that and for every unit increase in x, the output decreases by 60 percent.. Enter your answer in form.

Given the functions: F(x) = 114 (3.1)^x G(x) = 20 + 0.79x H(x) = 84 (0.91)^x K(x) = 10.3 - 10.7x As , which function(s) approach 0? Select all that apply.

Alice invests $18,000 in an account offering 2.5% interest compounded monthly (12 times per year). How many years until the account value reaches $20,000? Round your answer to the nearest year.

The function represents the decay of the Asian beetle population in Wisconsin where T represents 5-year intervals. Create an equivalent function where T represents 1-year intervals. Round the decay factor to 3 decimal places.

For the exponential function given, identify A) the initial value and B) the growth factor.

For the exponential function given find the y-intercept. Write your answer as an ordered pair (x,y).

Choose the description that best describes the exponential function, .

For an exponential function, where x is measured in months and and , which of the following is the monthly growth factor of the function (Rounded to 2 decimal places.)?

Peru's population increased from 28.3 million to 28.7 million in 2006. Assuming this (exponential) growth continues, to the nearest year how many years will it take for the population to double?

Alice invests $9,000 in an account offering 7.5% interest compounded daily (365 times per year). Find the value of the account after 10 years. Round your answer to the nearest cent.

Pat recently inherited a large amount of money and wants to put some away for her child's college education. Pat figures her daughter will need $40,000 for college at age 18. Her daughter is now 12 years old and Pat can invest the money at 10.3% compounded Continuously. How much should Pat invest now to reach her goal? (Round the answer to the nearest penny.)

The half-life of penicillin in a beef cow is approximately 30 hours. If the acceptable level for butchering of 0.5 mL, and the beef cow is administered 25 mL of penicillin, will it be at an acceptable level to butcher after 7 days?

The half-life of Fluorine 18 is 1.82 hours. If a sample initially contains 6,400 atoms, how many atoms will be left after 3.64 hours? Round the answer to the nearest whole number if necesasry.

If the half-life of francium is 21 minutes, how much of a 4,000 gram sample would be left after 20 minutes? (Round the answer to the nearest gram.)

The cost of college tuition increases about 3.2% each year. If the average cost of tuition is $10,500 in 2007, find a function that gives the average tuition, T, as a function of the years after 2007, y, (Write your answer in form.)

Find the effective interest rate of an account that pays 8% interest compounded daily (365 times each year). Write your answer as a percent rounded to 2 decimal places, such as 4.13%.

The following function gives the value, V, of an investment as a function of y, the years since the original investment: Find the doubling time to the nearest year.