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Find the equation of the line tangent to the graph of f at the indicated value of X. f(x) = 7 ex + 13x; x=0 . . . . . y = 20x + 7\fSuppose the quantity (in grams) of a radioactive substance present at time t is Q(t) = 1000 (5 a. How much will be present in 5 months? b. How long will it take to reduce the substance to 8 grams? - 0.3t) where t is measured in months. a. There will be |:| grams of the substance present in 5 months. (Round to the nearest gram as needed.) b. It will take |:| months to reduce the substance to 8 grams. (Round to the nearest month as needed.) The exponential model A = 131.9 e .0 describes the population, A, of a country in millions, t years after 2003. Use the model to determine the population of the country in 2003. The population of the country in 2003 was million.Graph the equation below using a calculator and point-bypoint plotting. Indicate the increasing and decreasing intervals. y = 5 In x Choose the correct graph below. OA. ,0 I1.\" Where is the graph increasing or decreasing? Select the correct choice below and ll in any answer box(es) in your choice, if necessary. O A- The graph increases on and decreases on (Type your answer in interval notation.) 3- The graph decreases on (0.32) but does not increase. (Type your answer in interval notation.) O C. The graph increases on but does not decrease. (Type your answer in interval notation.) O D. The graph neither increases nor decreases. Use the properties of logarithms to write the expression as a sum, difference, or product of simpler logarithms. For example, log 2 (13x) = 2 log 23 + log 2x. 3p log 3 4k Identify the properties that must be applied to rewrite the expression. Let x and y be any positive real numbers and r be any real number. Let a be a positive real number, a # 1. Select all that apply. A. log ax' = rlog aX B. log axy = log ax + log ay c. log av - = log aX - log ay D. log a a = 1 Write the expression as a sum, difference, or product of simpler logarithms. 3p log 3 4k