solve the following 3. Since g(x)-mx+b In(Cx)), we suspect that f(x)c)Ca. We can rewritefx) C2/ for constants C,k. Then gx) In))-x + In(c). In(2) a. Write out the algebra that brings us frome to C...
3. Since g(x)-mx+b In(Cx)), we suspect that f(x)c)Ca. We can rewritefx) C2/ for constants C,k. Then gx) In))-x + In(c). In(2) a. Write out the algebra that brings us frome to C2** (Hint: This only relies or properties of exponents and the fact that ein 2 = 2. So, look at the algebra cheat sheet) b. By comparing the two expresSons for g(x), find k and C. Round to the first decimal place. (Note: ax + b = cx + d implies a = c and b = d.) Write down the function f(x).Sketch a curve through the data points in 1 to graph f. c. State three contexts from which the above data for f(x) could have come from. For example, could this represent the decline of a population? Could this represent the decay of a radioactive element? Etc. Please elaborate a little. What would x represent? 4. 5. Construct the table, set of ordered pairs, and graph for the inverse, fa), off(x). State the meaning of the inverse function in context to one of the scenarios you gave in 5 6. Compare the tables, sets of ordered pairs, and graphs for f (xandf(x)and describe the similarities and differences. Elaborate. Do you have symmetry? What is the only difference between the ordered pairs between the two? What is the difference in the rows and columns of the table data? What can be generalized here about the relationship between logarithms and exponentials as well as fand f"1? Solve the following equation:f(x)=2f(0)=65 and the equation f-i(x)=45tate what the solutions mean in one of the contexts you gave in 5 7.
3. Since g(x)-mx+b In(Cx)), we suspect that f(x)c)Ca. We can rewritefx) C2/ for constants C,k. Then gx) In))-x + In(c). In(2) a. Write out the algebra that brings us frome to C2** (Hint: This only relies or properties of exponents and the fact that ein 2 = 2. So, look at the algebra cheat sheet) b. By comparing the two expresSons for g(x), find k and C. Round to the first decimal place. (Note: ax + b = cx + d implies a = c and b = d.) Write down the function f(x).Sketch a curve through the data points in 1 to graph f. c. State three contexts from which the above data for f(x) could have come from. For example, could this represent the decline of a population? Could this represent the decay of a radioactive element? Etc. Please elaborate a little. What would x represent? 4. 5. Construct the table, set of ordered pairs, and graph for the inverse, fa), off(x). State the meaning of the inverse function in context to one of the scenarios you gave in 5 6. Compare the tables, sets of ordered pairs, and graphs for f (xandf(x)and describe the similarities and differences. Elaborate. Do you have symmetry? What is the only difference between the ordered pairs between the two? What is the difference in the rows and columns of the table data? What can be generalized here about the relationship between logarithms and exponentials as well as fand f"1? Solve the following equation:f(x)=2f(0)=65 and the equation f-i(x)=45tate what the solutions mean in one of the contexts you gave in 5 7.