1. Find the equation of the line tangent to the graph of f(x) = (Inx) ? at x=4. 2. In 2004, an art collection paid $120,089,000 for a particular painting. The same painting sold for $31,000 in 1950. Find the exponential growth rate k, to three decimal places, and determine the exponential growth function V, for which V(t) is the painting's value, in dollars, t years after 1950. How long after 1950 will the value of the painting be $3 billion? 3. The size of a certain insect population is given by P(t) = 100 e .021, where t is measured in days. At what time will the population equal 400? 4. Uranium-238 (U-238) has a half- life of 4.5 billion years. Geologists find a rock containing a mixture of U-238 and lead, and determine that 56% of the original U-238 remains: the other 44% has decayed into lead. How old is the rock? ( Round to three decimal places as needed) 5. A concentration of a drug in the body decreases exponentially after a dosages given. In one clinical study, adult subjects averaged 14 micrograms/ millileter (mcg/ml) of the drug in the body plasma 1 hr after a 1000 mg dosage and 5 micrograms/millileter 5 hr after dosage. Find the value k, and write an equation for an exponential function that can be used to predict the concentration of the drug, in micrograms/ millileter, t hours after a 1000-mg dosage. 6. Find any critical values and any relative extrema. g(x) = - x3+12x -18. 7. Find any critical values: t(x) = x3 +x +10 8. Find any relative extrema of the function, g(x) = 23 + 10x + x2 9. For the function K(x) = 3x* + 8x3, identify the intervals where the function is concave up or concave down. 10. For the rational function g(x) = x/ ( x2+ 25), identify intervals where the function is concave up or concave down