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Find the equation of the line that goes through the points (4, –1) and (2, –5). use slope formula,equation,to find the slope of a line that passes through the points. m = use slope-intercept form, y = mx + b, to find the y-intercept (b) of the line. b = write the equation in slope-intercept form, y = mx + b.

Let f (x) = x e8x. find a formula for the nth derivative of f, where n is any positive integer. use x and n in your answer if needed. f (n)(x) =

The rate of decay of a radioactive substance depends upon the amount present initially. the mass y (mg) of the radioactive substance cobalt-60 present in a sample at time t (years) is represented by the exponential equation y=50e −0.1315 t . answer the following questions in complete sentences. 1. how does the exponential equation above compare to the equation for simple interest that is compounded continuously? explain the similarities. 2. what is the initial amount of cobalt-60 in the sample? 2. how much cobalt-60 is left after 8.4 years? show your work. 3. what would be the y-intercept of the graph? what does it represent? 4. after how many years will the amount of cobalt-60 left be 6.25 mg? explain what happens to the cobalt-60 after 50 years? 5. discuss some “real-world” examples and uses of cobalt-60