- #1
brandy
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^^^
what does b indicate for y=(A^x)^b
i was thinking it should be the rate of rate of change or something, idk.
what does b indicate for y=(A^x)^b
i was thinking it should be the rate of rate of change or something, idk.
What do you mean by "what does b indicate? It is a number multiplying x! It is true that, for that particular function, y'= be^(bx) so y'= by. In this particular example b is again what Euclideus said: "the exponential rate of growth (or decay)". (He said that it was part of that along with ln A in e^(b ln(A) x) so you have just replaced his "b ln(A)" with b.brandy said:so wat does b indicate for y=e^(bx)
The variable b in this equation represents the exponent to which the base A is raised to. It determines the rate of change of the function y with respect to the variable x.
Changing the value of b will result in a vertical stretch or compression of the graph of the function. A larger value of b will result in a steeper curve, while a smaller value of b will result in a flatter curve.
Yes, b can be a negative or a fraction in this equation. A negative b value will result in a reflection of the graph across the x-axis, while a fraction will result in a horizontal stretching or compressing of the graph.
A in this equation represents the base of the exponential function. It can be any positive number greater than 0, and it determines the initial value of the function at x=0. Changing the value of A will result in a vertical shift of the graph.
In a real-world scenario, b can represent a growth rate or decay rate. For example, if y represents the population of a bacteria colony and x represents time, then b would represent the growth rate of the colony. Similarly, in financial applications, b can represent an interest rate or inflation rate.