What is the y-intercept of all exponential growth functions?

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Answer 1 · 2018-05-28T16:05:29

#(0,1)#

the general formula for any exponential function is #a^x#.

(e.g. #2^x, 3^x#)

the #y#-intercept of a graph is the point where it touches the #y#-axis. the #y#-axis touches the #x#-axis when #x = 0#.

the #y#-intercept of the graph is the point where #x = 0# and #y# is a certain value.

if the exponential function is #a^x#, then the #y#-intercept is the point where #a^x = a^0#.

any number raised to the power of #0# gives #1#.

hence #a^0# will always be #1#.
is #y = a^x#, then the #y#-intercept is #(0, a^0)#, which is #(0,1)#.