Use the fact that y = 4 + 2 and y = log4 (x - 2) are inverses of each other to find dy for y = log4 (x - 2) using the Inverse Function Theorem, showing your process. da Then check that you got the correct derivative using other differentiation rules, showing your process.

Due to depreciation, the value of an automobile t years after purchase is f(t) = ((900 + 6t / 1+0.5t) + 50) dollars a) What is the value of the automobile when new? b) As t increases, what happens to the value of the new automobile? c) What is the value of the automobile after 6 years?

The U.S. population can be modeled by the function y=165.6x¹.345, where y is in thousands and x is the number of years after 1800. (a) What was the population in 1970, according to this model? (b) is the graph of this function concave up or concave down? What does this mean? (c) Use numerical or graphical methods to find when the model estimates the population was 94,150,000. (a) According to the model, the population in 1970 was thousands. (Round to the nearest integer as needed.)

Solve for f:1/p+1/q=1/f   Show your work