Chapter 1.3, Problem 49E

Physicists using the radioactivity equation y = yo e - kt call the number 1 the mean life of a radioactive nucleus. Show that 95% of the radioactive nuclei originally present in a sample will disintegrate within three mean lifetimes, i.e., by time t=. Thus, the mean life of a k nucleus gives a quick way to estimate how long the radioactivity of a sample will last. ..... - kt If 95% of a sample has decayed, there is 5% remaining. How can you use the radioactivity equation y(t) = yo e to find when 5% of the sample is remaining? A. Set y(t) equal to 0.05 and solve for t. B. Evaluate y(0.05). C. Set y(t) equal to 0.05y, and solve for t. D. Evaluate y(5). Perform the operation determined in the previous step. Yo e - kt 0.05yo - kt e = 0.05 Divide both sides by yo: = In 0.05 Take the natural logarithm of each side. In 0.05 t = Solve for t. Approximate In 0.05. In 0.05 x (Round to three decimal places as needed.) Since this value is approximately equal to then 95% of a sample will…

Determine whether the table could represent a function that is linear, exponential, or neither. If the function is exponential or linear, find a function that passes through the points. a) x 1 2 3 4 f(x) 70 49 34.3 24.01 b) x 1 2 3 4 f(x) 10 20 30 40   2)The fox population in a certain region has an annual growth rate of 5% per year. In the year 2012, there were 20460 fox counted in the area. Write a function, f(t), that models the number of fox in the population at tt years after 2012. Assume a continuous growth rate.   3) Adam wants to save $51000 for a down payment on a home. How much will he need to invest in an account with 7.9% APR, compounding daily, in order to reach his goal in 4 years? 4) Write an equatio for the graph. (PHOTO ATTACHED)   NOT GRADED JUST CHECKING ANSWERS! THANK YOU

Model the data using an exponential function f(x) = Abx. f(x) = = X f(x) 01 2 125 25 5

Determine whether each table or rule represents a linear function, an exponential function, or neither. 1. 3 4 6 y 2 8. 16 32 64 2 3 4 y 1 7 10 13 16 y = 4(0.2)* y = 3(2)* y = 5x - 8 y = 5(1.07)- :: Exponential Function :: Linear Function :: Neither CREATIVE

Use log. Differantion

Sketch the graph of the exponential function f(x) = 3* + 2. Write down the domain and range of f from the graph in the box given below: Insert your name and ID and upload the graph.

22. Per capita income. In 2009, U.S. per capita personal income I was $48,040. In 2012, it was $52,430. (Source data.worldbank.org.) Assume that the growth of U.S. per capita personal income follows an exponential model. a) Letting i = 0 be 2009, write the function. b) Predict what U.S. per capita income will be in 2020. c) In what year will U.S. per capita income be double that of 2009?

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Math 116 Section 6.3 Example 1 Write the following in exponential form. A. log (√6) = 12 B. log3 (9) = 2 C. log101000000 = 6 D. log525 = 2