Question

1. if $g(x)=2(5)^x$, which of the following is the value of $g(-3)$?

(1) $-150$
(3) $\frac{2}{15}$
(2) $-30$
(4) $\frac{2}{125}$

Explanation:

Step1: Substitute \( x = -3 \) into \( g(x) \)

We have the function \( g(x)=2(5)^{x} \). To find \( g(-3) \), we substitute \( x = -3 \) into the function. So we get \( g(-3)=2(5)^{-3} \).

Step2: Use the negative exponent rule

Recall the negative exponent rule: \( a^{-n}=\frac{1}{a^{n}} \) (where \( a
eq0 \) and \( n \) is a positive integer). Applying this rule to \( 5^{-3} \), we have \( 5^{-3}=\frac{1}{5^{3}} \). And \( 5^{3}=5\times5\times5 = 125 \), so \( 5^{-3}=\frac{1}{125} \).

Step3: Calculate the value of \( g(-3) \)

Now, substitute \( 5^{-3}=\frac{1}{125} \) back into \( g(-3)=2(5)^{-3} \). We get \( g(-3)=2\times\frac{1}{125}=\frac{2}{125} \).

Answer:

(4) \(\frac{2}{125}\)