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Question
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what is the starting value in the equation $f(x) = 11(1.7)^{x - 1}$? (1 point)
the starting value is \boxed{}.
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Step1: Recall the form of exponential function
The general form of an exponential function is \( f(x)=a(b)^{x - c}+d \), and the starting value (initial value) is the value of the function when \( x \) takes the value that makes the exponent zero (usually when \( x = c \) for the form \( f(x)=a(b)^{x - c} \)). For the function \( f(x)=11(1.7)^{x - 1} \), we need to find the value when \( x = 1 \) (because when \( x=1 \), the exponent \( x - 1=0 \)).
Step2: Substitute \( x = 1 \) into the function
Substitute \( x = 1 \) into \( f(x)=11(1.7)^{x - 1} \), we get \( f(1)=11\times(1.7)^{1 - 1} \). Since any non - zero number to the power of 0 is 1, \( (1.7)^{0}=1 \). Then \( f(1)=11\times1 = 11 \).
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