Question

How do I find the exponential function that passes through the point \[(4,2)\]?

Answer 1

Hint: Let us consider the exponential equation\[y = {a^x}\], where \[a\] is a constant coefficient. The equation passes through the point. From, there we can find the value of \[a\]. Finally we can get the exponential function.

Complete Step by Step Solution:
It is given that, the point is \[(4,2)\]
We have to find the exponential function that passes through the point \[(4,2)\].
Let us consider the exponential equation\[y = {a^x}\], where \[a\] is a constant coefficient.
The equation passes through the point \[(4,2)\].
So, we have, \[2 = {a^4}\]
Simplifying we get,
\[a = \sqrt[4]{2}\]
Substitute the value of \[a\]in the general form of equation we get,
\[y = {(\sqrt[4]{2})^x}\]

Hence, the exponential function that passes through the point \[(4,2)\]is \[y = {(\sqrt[4]{2})^x}\].

Note: An exponential function is a Mathematical function in form \[f(x) = {a^x}\], where “\[x\]” is a variable and “\[a\]” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
An exponential function is defined by the formula \[f(x) = {a^x}\], where the input variable \[x\] occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the \[x\].
The exponential function is an important mathematical function which is of the form \[f(x) = {a^x}\]
Where \[a\]>0 and a is not equal to 1.
\[x\] is any real number.
If the variable is negative, the function is undefined for -1 < \[x\] < 1.
Here,
“\[x\]” is a variable
“\[a\]” is a constant, which is the base of the function.
An exponential curve grows, or decay depends on the exponential function. Any quantity that grows or decays by a fixed per cent at regular intervals should possess either exponential growth or exponential decay.