Answer :
The function [tex]A(t)=676\pi (t+1)[/tex].
What is a function?
- A function from a set X to a set Y allocates one element of Y to each element of X.
- The set X is referred to as the function's domain, while the set Y is referred to as the function's codomain.
- Functions were originally the idealization of how a varying quantity depends on another quantity.
To find the function [tex]A(t)[/tex] :
The area of a circle is expressed as;
[tex]A=\pi r^{2}[/tex]
Where A = Area
r = radius
From the case above.
The radius of the ripple is a function of time:
[tex]r=r(t)=26\sqrt{t+1}[/tex]
So,
[tex]A(t)=\pi [r(t)]^{2}[/tex]
Substituting [tex]r(t)[/tex],
[tex]A(t)=\pi (26\sqrt{t+1} )^{2} \\A(t)=\pi (676(t+1))\\A(t)=\pi (26\sqrt{t+1} )^{2} \\A(t)= 676\pi (t+1)[/tex]
Therefore, the function [tex]A(t)=676\pi (t+1)[/tex].
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The question you are looking for is here:
A raindrop hitting a lake makes a circular ripple. Suppose the radius, in inches, grows as a function of time in minutes according to r(t)=26t+1−−−−√, and answer the following questions. Find a function, A(t), for the area of the ripple as a function of time.