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Determine a possible equation of a exponential function that satisfies 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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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. ANSWER
Visual check
Plot y = -3*2^(-x) + 5 (red) and y = 5 (green)
Solved and checked.
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It is one of many possible examples. There are many (infinitely many) other functions with similar properties.