Q: Is it an exponential function if you add 5 to the x value each time?

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The number of atoms that decay in a certain time is proportional to the amount of substance left. This naturally leads to the exponential function. The mathematical explanation - one that requires some basic calculus - is that the only function that is its own derivative (or proportional to its derivative) is the exponential function (or a slight variation of the exponential function).

Yes. Anything that multiplies repeatedly like that is exponential, also sometimes referred to as geometric.

With exponentiation functions, the rate of change of the function is proportional to it present value.A function f(x) = ax is an exponentiation function [a is a constant with respect to x]Two common exponentiation functions are 10x and ex. The number 'e' is a special number, where the rate of change is equal to the value (not just proportional). When the number e is used, then it is called the exponential function.See related links.

They are similar because the population increases over time in both cases, and also because you are using a mathematical model for a real-world process. They are different because exponential growth can get dramatically big and bigger after a fairly short time. Linear growth keeps going up the same amount each time. Exponential growth goes up by more each time, depending on what the amount (population) is at that time. Linear growth can start off bigger than exponential growth, but exponential growth will always win out.

That means that the growth is equal to, or similar to, an exponential function, which can be written (for example) as abx, for constants "a" and "b". One characteristic of exponential growth is that the function increases by the same percentage in the same time period. For example, it increases 5%, or equivalently by a factor of 1.05, every year.

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An exponential growth function actually describes a quantity that increases exponentially over time, with the rate of increase proportional to the current value of the quantity, resulting in rapid growth. The formula for an exponential growth function is y = a * (1 + r)^t, where 'a' is the initial quantity, 'r' is the growth rate, and 't' is time.

Exponential growth in mathematics refers to how the growth rate of a value is proportional to the current value. Therefore, as the current value increases, the growth rate increases by a larger amount each time.

The exponential function describes a quantity that grows or decays at a constant proportional rate. It is typically written as f(x) = a^x, where 'a' is the base and 'x' is the exponent. For example, if we have f(x) = 2^x, each time x increases by 1, the function doubles, showing exponential growth.

The number of atoms that decay in a certain time is proportional to the amount of substance left. This naturally leads to the exponential function. The mathematical explanation - one that requires some basic calculus - is that the only function that is its own derivative (or proportional to its derivative) is the exponential function (or a slight variation of the exponential function).

Yuo cannot include a graphical illustration here. Take a look at the Wikipedia, under "exponential function" and "logistic function". Basically, the exponential function increases faster and faster over time. The logistics function initially increases similarly to an exponential function, but then eventually flattens out, tending toward a horizontal asymptote.

There is no such thing. "Exponential growth" implies that there is some function - a variable that depends on another variable (often time).

True

False

Yes.

Yes.

True

An exponential function represents this pattern, since each hour the bacteria population is being multiplied by the same factor (0.5 in this case). The general form of the function would be: B(t) = B0 * (0.5)^t, where B(t) is the number of bacteria at time t and B0 is the initial number of bacteria.