DAY 1 1. Solve the exponential equation 32 = 8 by changing the bases. - in exponential for wit 2. Solve the exponential equation 25*+4 = 6252% by changing the bases. old. growth of a tree is it cars. Estimate the3. Trinh has decided to save money to buy a new computer. She invests $800 in an account that earns 5.0% per year, compounded quarterly. Determine how long she needs to invest her money until she has $1000. Explain the process you used. 12 Day 2 1. Rewrite the logarithmic equation 109R M = -H in exponential form with positive exponents and no fractions. 12 Complete questions 2 and 3 online. 4. In the beginning of this lesson the idea that the growth of a tree could be modelled using a logarithmic function was introduced. A possible logarithmic function that could model the growth of a tree is h = 4 log3 t, where h is the height of the tree in metres and t is the time in years. Estimate the approximate height of the tree to the nearest tenth of a metre after 10 yr. Explain the reasoning for your estimation. 125. The formula for the Richter magnitude, M, of an earthquake is M = 109 A g A , where A is the amplitude of the earthquake and A, is the amplitude of a standard earthquake with magnitude of 0. In 2011, an earthquake occurred off the Pacific coast of the Tohoku region of Japan. This earthquake, which measured 9.0 on the Richter scale, is one of the five most powerful earthquakes in the world since modern record-keeping began in 1900. By comparison, one of the largest earthquakes to hit Alberta was a magnitude 4.7 earthquake. This earthquake occurred in 1984, on the border between British Columbia and Alberta, just north of Waterton Lakes National Park. Determine how many times larger in amplitude the Tohoku earthquake was compared to the Alberta quake. Answer to the nearest ten thousand. 12 Day 3&4 1. Consider the functions f(x) = log2 x and g(x) = -4log, (x-3) + 7. 12 a. Find the domain and range for both functions. domain range f (x) g(x) b. Explain how the graph g(x) can be described as a transformation of f(x). 12num lo 2. The graph of f(x) = log3 x is vertically stretched about the x-axis by a factor of 2 . horizontally stretched about the y-axis by a factor of 3 . translated 5 units to the right and 2 units down If the equation of the transformed image is written in the form g (x) = alog3 b(x -c)]+ d, determine the values of a, b, c, and d. Then write the equation of g(x). 13 3. The slope of a beach is influenced by the local tides, wind and wave patterns, and the size of the sand particles on the beach. In general, as the diameter in millimetres, d, of the average size of the particles on the beach increases, the slope of the beach, s, increases according to the formula s(d) = 0.159 + 0.1181 log d. a. Describe the graph of the function s(d) as compared to the graph of f (d) = log d using transformations terminology. 12 b. If the slope of a particular beach is 0.005 (about a 1-m vertical climb for every 200 m in the horizontal direction), determine the average diameter (in millimetres) of a grain of sand on the beach. Round your answer to 4 decimal places. 11