Answer:
(d) f(x) = 1.5^x, g(x) = 1.6^x, h(x) = 1.7^x
Explanation:
You want to find the possible functions for the graph showing f(x), g(x), and h(x) as exponential growth functions with h(x) growing the fastest and f(x) growing the slowest.
Exponential growth
An exponential growth function can be of the form ...
f(x) = b^x
where b > 1. The larger the value of b, the faster the growth.
Choices
The bases (b) of the functions f, g, h in order are ...
a) 1.7, 1.6, 1.5
b) 0.7, 0.6, 0.5 . . . . . . exponential decay functions
c) 1.6, 1.5, 1.7
d) 1.5, 1.6, 1.7 . . . . . . . f(x) grows slowest; h(x) grows fastest
The functions in order of increasing growth rate are f, g, h, so the bases need to be in increasing order. The only feasible answer choice is ...
(d) f(x) = 1.5^x, g(x) = 1.6^x, h(x) = 1.7^x
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Additional comment
The attachment shows a graph of these functions. Their growth is in the right order, but the curves clearly do not match those shown in the problem statement. One could say the match is "conceptual," rather than actual.
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