What you wrote is e4 - x + 2, which is a straight line whose slope is -1.j9mom said:Homework Statement
State whether (e^4-x) + 2 is an exponential growth function or an exponential decay function. Explain why.
You need parentheses here, too. f(x) = ae^(kx).j9mom said:Homework Equations
I want to use the formula f(x) = ae^kx where a>0, and k<0.
j9mom said:The Attempt at a Solution
I know it is an exponential decay formula because the limit as x goes to -inf. = inf. and the limit as x goes to inf. = 2. But I do not know how to describe what a and k are in this equation to show it is an exponential decay function.
Exponential growth or decay is a mathematical concept that describes a rapid increase or decrease in a quantity over time, where the rate of change is proportional to the current value of the quantity.
In linear growth or decay, the quantity changes at a constant rate over time. In exponential growth or decay, the rate of change increases or decreases as the quantity increases or decreases, resulting in a rapidly accelerating or decelerating trend.
Examples of exponential growth include population growth, compound interest in finance, and the spread of infectious diseases. Examples of exponential decay include radioactive decay and the decrease in value of a car over time.
The formula for exponential growth is y = ab^x, where a is the initial quantity, b is the growth rate, and x is the time. The formula for exponential decay is y = ab^(-x), where a is the initial quantity, b is the decay rate, and x is the time.
The rate of exponential growth or decay can be affected by various factors such as the initial quantity, the growth or decay rate, and external influences like competition, resources, and limiting factors. Additionally, for exponential decay, the half-life of the quantity is an important factor that determines the rate of decay.