Answer :
the most likely function for the given graph is [tex]f(x) = 20e^x[/tex], which corresponds to choice B.
The graph in question appears to be an exponential function with a steep initial growth rate. To determine which of the given functions matches the graph, let's analyze each option:
A. [tex]f(x) = e^{20x}[/tex]
When x = 0, [tex]f(x) = e^{20 * 0} = 1[/tex]. This matches the point (0, 20).
B. [tex]f(x) = 20e^x[/tex]
When x = 0, [tex]f(x) = 20 * e^0 = 20 * 1 = 20[/tex]. This also matches the point (0, 20).
C. [tex]f(x) = 20^x[/tex]
When x = 0, [tex]f(x) = 20^0 = 1[/tex]. However, this does not match the point (0, 20).
D. [tex]f(x) = 20^{20x}[/tex]
When x = 0, [tex]f(x) = 20^{20 * 0} = 20^0 = 1.[/tex] This also matches the point (0, 20).
Based on the analysis, both options A and D yield the point (0, 20), but option B is the best fit for the graph shown because it also matches the point (0, 20) and exhibits a steep initial growth rate. Therefore, the most likely function for the given graph is [tex]f(x) = 20e^x[/tex], which corresponds to choice B.
To know more about graph:
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Answer:
B
Step-by-step explanation:
we take the only point we know
(0,20)
in A when x =0
[tex]f(x)=e^{20x} =e^{20*0}=1[/tex]
in B when x=0
[tex]f(x)=20e^x=20e^0=20*1=20[/tex]
fits
in C
[tex]f(x)=20^x=20^0=1[/tex]
in D
[tex]f(x)=20^{20x}=20^{20*0}=20^0=1[/tex]
so the only choice is B
