exponential decay doesnt have to have a decreasing halving time. it just decays at a certain percentage every time, which might be 50% or might not
True
positive
A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. The time required for the decaying quantity to fall to one half of its initial value.Radioactive decay is a good example where the half life is constant over the entire decay time.In non-exponential decay, half life is not constant.
a variable
$75
False
That would be an exponential decay curve or negative growth curve.
True
depends it can be true or false Apex: False
An exponential decay function describes a process where a quantity decreases at a rate proportional to its current value, leading to a consistent halving time. This means that after each fixed interval, the quantity reduces to half of its previous amount. For example, in radioactive decay, the halving time remains constant regardless of how much of the substance is left, illustrating the characteristic nature of exponential decay. Overall, it models many real-world phenomena where resources diminish over time.
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.
positive
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.
A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. The time required for the decaying quantity to fall to one half of its initial value.Radioactive decay is a good example where the half life is constant over the entire decay time.In non-exponential decay, half life is not constant.
A graph can effectively illustrate exponential growth by plotting data points that represent a quantity over time on a Cartesian plane. The x-axis typically represents time, while the y-axis represents the quantity increasing exponentially. As the data progresses, the graph will display a curve that rises sharply, indicating that the growth rate accelerates as the quantity increases. This visual representation helps highlight the difference between linear and exponential growth, making the concept more comprehensible.
A quantity that has a constant halving time is typically represented by exponential decay. This means that the quantity decreases by half over a consistent time interval, regardless of its current value. Common examples include radioactive decay, where the half-life remains constant, and certain population dynamics in biology. The characteristic of constant halving time indicates a predictable and exponential decline in the quantity over time.
The quantity is decreasing.