A market analyst working for a small-appliance manufacturer finds that if the firm produces and sells x blenders annually, the total profit (in dollars) is P(x) = 8x + 0.3x2 − 0.0013x3 − 374. Graph the function P in an appropriate viewing rectangle and use the graph to answer the following questions. (a) When just a few blenders are manufactured, the firm loses money (profit is negative). (For example,  P(10) = −265.30,  so the firm loses $265.30 if it produces and sells only 10 blenders.) How many blenders must the firm produce to break even? (Round your answer to the integer that gives the company the least positive profit.) (b) Does profit increase indefinitely as more blenders are produced and sold? Yes No     If not, what is the largest possible profit the firm could have? (Round your answer to the nearest cent. If an answer does not exist, enter DNE.) $

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Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.