The formula for the surface area N(t) of the balloon after t seconds is [tex]N(t) = \frac {64}9\pi t^2[/tex]
How to determine the surface area?
We have:
[tex]S(r) = 4\pi r^2[/tex]
Also, we have:
[tex]P(t) = \frac 43t[/tex]
The above can be rewritten as:
[tex]r = \frac 43t[/tex]
Substitute [tex]r = \frac 43t[/tex] in S(r) to determine the function N(t)
[tex]S(r) = 4\pi (\frac 43t)^2[/tex]
Express as N(t)
[tex]N(t) = 4\pi (\frac 43t)^2[/tex]
Expand the exponent
[tex]N(t) = 4\pi *\frac {16}9t^2[/tex]
Evaluate the product
[tex]N(t) = \frac {64}9\pi t^2[/tex]
Hence, the formula for the surface area N(t) of the balloon after t seconds is [tex]N(t) = \frac {64}9\pi t^2[/tex]
Read more about composite functions at:
https://brainly.com/question/10687170
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