An exponential function is a function of the form where and are real numbers and is positive. Exponential functions are used to model relationships with exponential growth or decay. Exponential growth occurs when a function's rate of change is proportional to the function's current value. Whenever an exponential function is decreasing, this is often referred to as exponential decay.
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Suppose that the population of rabbits increases by 1.5 times a month. When the initial population is 100, what is the approximate integer population after a year?
The population after months is given by Therefore, the approximate population after a year is
Suppose that the population of rabbits increases by 1.5 times a month. At the end of a month, 10 rabbits immigrate in. When the initial population is 100, what is the approximate integer population after a year?
Let be the population after months. Then and from which we have Then the population after months is given by Therefore, the population after a year is given by
Suppose that the annual interest is 3 %. When the initial balance is 1,000 dollars, how many years would it take to have 10,000 dollars?
The balance after years is given by To have the balance 10,000 dollars, we need Therefore, it would take 78 years.
The half-life of carbon-14 is approximately 5730 years. Humans began agriculture approximately ten thousand years ago. If we had 1 kg of carbon-14 at that moment, how much carbon-14 in grams would we have now?
The weight of carbon-14 after years is given by in grams. Therefore, the weight after 10000 years is given by Therefore, we would have approximately 298 g.