However, once you start learning some calculus, you'll see that it is more natural to get rid of the base parameter $b$ and instead use the constant $k$ to make the function grow or decay faster or slower. If we set $b=1$, we'd have the boring function $f(x)=1$, or, if we set $b=0$, we'd have the even more boring function $f(x)=0$. If we didn't have calculus, we'd probably choose $b=2$, writing our exponential function as $f(x)=2^$.Or, since we like the decimal system so well, maybe we'd choose $b=10$ and write our exponential function of $f(x)=10^$.
The function $$g(x)=\left(\frac\right)^x$$ is an example of exponential decay.For example, the function $$h(x)=2^$$ is also an exponential function. sie sucht sie Offenbach am Main It just grows faster than $f(x)=2^x$ since $h(x)$ doubles every time you add only $1/3$ to its input $x$.You can change the value of $c$ by dragging the red point.You can change range of the $x$ and $y$-axes buttons labeled $x $, $x-$, $y $, and $y-$.
Single exponential decay function
Since it is silly to have both parameters $b$ and $k$, we will typically eliminate one of them.The easiest thing to do is eliminate $k$ and go back to the function $$f(x)=b^x.$$ We will use this function a bit at first, changing the base $b$ to make the function grow or decay faster or slower.To change the value of $f(0)$, you can allow scaling of the function by clicking the corresponding checkbox.Then, the function changes to $f(x)=c b^$ with an additional parameter $c$ that scales (multiplies) the whole function so that $f(0)=c$.A simple example is the function $$f(x)=2^x.$$ As illustrated in the above graph of $f$, the exponential function increases rapidly.