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It can be growth or decay - it depends on whether n is positive (growth) or negative (decay).

Q: Is the equation P500(1.03) with an exponent of n a model of Growth or Exponential Decay?

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That you have an exponential function. These functions are typical for certain practical problems, such as population growth, or radioactive decay (with a negative exponent in this case).

If the exponent has the variable of time in it, then it will be either exponential growth (such as compound interest for example), or exponential decay (such as radioactive materials, or a capacitor discharging). If the time constant (coefficient of the time variable) is positive then it is growth, if the time constant is negative, then it is decay.

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.

Any number below negative one.

implementation of exponential groth

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Reverend Thomas Malthus developed the concept of Exponential Growth (another name for this is Malthusian growth model.) However the mathematical Exponent function was already know, but not applied to population growth and growth constraints. Exponential Decay is a natural extension of Exponential Growth

It is not enough to look at the base. This is because a^x is the same as (1/a)^-x : the key is therefore a combination of the base and the sign of the exponent.0 < base < 1, exponent < 0 : growth0 < base < 1, exponent > 0 : decaybase > 1, exponent < 0 : decaybase > 1, exponent > 0 : growth.

That you have an exponential function. These functions are typical for certain practical problems, such as population growth, or radioactive decay (with a negative exponent in this case).

If the exponent has the variable of time in it, then it will be either exponential growth (such as compound interest for example), or exponential decay (such as radioactive materials, or a capacitor discharging). If the time constant (coefficient of the time variable) is positive then it is growth, if the time constant is negative, then it is decay.

both have steep slopes both have exponents in their equation both can model population

If your equation is y=0.682x then yes

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.

Any number below negative one.

implementation of exponential groth

The r value in the exponential equation is the rate of natural increase expressed as a percentage (birth rate - death rate). So the math includes the birth rate and the death rate when implementing the equation. Students may have a hard time understanding that population growth is controlled not only by birth and death rates but also by the present population. The mathematics of exponential growth govern the prediction of population growth. Your welcome Ms. Musselma...'s class.

Exponential growth does not have an origin: it occurs in various situations in nature. For example if the rate of growth in something depends on how big it is, then you have exponential growth.

Even numbers, Equilateral triangle, Exponential growth curve...