Question 1180766
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Determine a possible equation of a exponential function that {{{highlight(cross(satisfy))}}} <U>satisfies</U> the following properties. 
Include a sketch of the function in your solution.
a) Its y-intercept is 2
b) It has a horizontal asymptote at y = 5
c) it is always increasing
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<pre>
y = ab^(-x) + c


Coefficient "a" must be negative (I will take it in the form  a = - A,  where A is positive).


The base "b" must be positive, and can be any positive number; I will take b = 2.


Coefficient "c" must be equal to 5.


     y = -Ab^(-x) + 5.


An additional condition is  -Ab^0 + 5 = 2,  which gives  A = 5 - 2 = 3.


Final function  y = -3*2^(-x) + 5.     <U>ANSWER</U>


                       Visual check


    {{{graph( 400, 400, -5, 5, -5, 10,        
              -3*2^(-x) + 5, 5
)}}}


          Plot y = -3*2^(-x) + 5 (red)  and  y = 5  (green)
</pre>

Solved and checked.


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It is one of many possible examples. There are many &nbsp;(infinitely many) &nbsp;other functions with similar properties.