Question 1042255
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A type of aquatic bird known as a cormorant is flying over open water and accidentally drops a small fish from a height of 30 feet. 
The distance the fish is from the water as it falls can be described by the function h(t)=-16t^2+30 where t= time in seconds. 
A seagull spies the falling fish and flies along a straight line to intercept the fish.  His line of flight represented by the 
linear equation g(t)=-8^t+15

PART 1 After how many seconds does the seagull catch the falling fish?  

PART 2 After the seagull catches the fish he changes his travel path to k(t)=-2t+12.The cormorant chases the seagull in an attempt 
to try to win back the fish,descending along the path -t^2+15.How many feet above the water will the cormorant catch up to the seagull?
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Sorry, the equation g(t) = {{{-8^t+15}}} is not linear.


<pre>
If it is g(t)=-8t+15, then the solution for Part 1) is

{{{-16t^2+30}}} = {{{-8t+15}}},

{{{16t^2 - 8t + 15}}} = {{{0}}},

t = {{{(8 +- sqrt(64+4*16*15))/32}}} = {{{(8 +- 32)/32}}}.

Only positive root is of interest: t = {{{5/4}}} seconds.

<U>Answer to Part 1)</U>.  t = {{{5/4}}} seconds.
</pre>


<TABLE> 
  <TR>
  <TD> 

{{{graph( 330, 330, -5.5, 5.5, -4.5, 35.5,
          -16x^2+30, -8x+15
)}}}


Plot h(t) = {{{-16t^2+30}}} (red) and g(t) = {{{-8t+15}}} (green)

  </TD>
  </TR>
</TABLE>