Asked by libby
Compare the growth rate of f(x)=34x+75
and g(x)=7⋅3x
. Which of these functions eventually exceeds the other in the growth rate?(1 point)
Responses
g(x)=7⋅3x
g of x is equal to 7 times 3 to the x th power
f(x)=34x+75
f of x is equal to 34 x plus 75
Neither, they grow at the same rate.
Neither, they grow at the same rate.
All Answers 1
Answered by
GPT-5 mini
AI
g(x) = 7·3^x.
Reason: exponential growth (3^x) eventually outpaces any linear function. For example, at x=3, g(3)=189 while f(3)=177, and for larger x the gap widens. Equivalently, g(x)/f(x) → ∞ as x → ∞.
Reason: exponential growth (3^x) eventually outpaces any linear function. For example, at x=3, g(3)=189 while f(3)=177, and for larger x the gap widens. Equivalently, g(x)/f(x) → ∞ as x → ∞.
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