How are linear and exponential functions similar and different. Discuss the relationship between the m and b in y= mx+b and the a and b or a and r in y= a (b)x or an= a1(r)x.
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Answers
Linear functions are functions in which the rate of change is constant. Because you are getting the same amount of money each day, your change in money is the same.
Doubling your initial one cent every day is an example of an exponential function. Exponential functions are functions in which the the rate of change is not constant (not adding the same ten dollars each day, in other words). In this case, the rate of change increases each time because you are getting more money each day (doubling your money). Exponential functions increase by the same percent each time. In your case, your money increases by 100% each day.
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Answer:
Linear functions are graphed as straight lines while exponential functions are curved. Linear functions are typically in the form y = mx + b, which is used to discover the slope, or simply the change in y divided by the change in x, while exponential functions are typically in the form y = (1 + r) x.