the function give by f(x)=a^x, where a>0 and a≠ 1
The function f(x) = a^x represents exponential growth or decay
The function f(x) = a^x represents exponential growth or decay. In this function, ‘a’ is the base and ‘x’ is the exponent. The base ‘a’ must be a positive number and not equal to 1.
When the base ‘a’ is greater than 1, the function f(x) = a^x represents exponential growth. As the exponent ‘x’ increases, the function value increases rapidly. For example, if a = 2, then f(x) = 2^x will have values like 2, 4, 8, 16, 32, and so on. This means that as ‘x’ gets larger, the function value grows exponentially.
On the other hand, when the base ‘a’ is between 0 and 1, the function f(x) = a^x represents exponential decay. As the exponent ‘x’ increases, the function value decreases rapidly. For example, if a = 0.5, then f(x) = 0.5^x will have values like 0.5, 0.25, 0.125, 0.0625, and so on. The function value decreases exponentially as ‘x’ increases.
It is important to note that in both cases, the function f(x) never equals 0 or becomes negative. The base ‘a’ determines the rate of growth or decay. If ‘a’ is closer to 1, the function will change more slowly, while if ‘a’ is farther from 1, the function will change more rapidly.
Overall, the function f(x) = a^x, where a > 0 and a ≠ 1, describes exponential growth or decay depending on the value of ‘a’.
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