Find the value of A that makes the following equation true for all values of x. 0.9^(60 x)=A^(x) Choose 1 answer: (A) A=0.9*60 (B) A=0.9^(60) (c) A=(60)/(0.9) (D) A=60^(0.9)

Understand and Identify Bases: Understand the equation and identify the bases. We are given the equation 0.9^(60x) = A^(x). We need to find the value of A such that this equation holds true for all x. To do this, we need to compare the bases of the exponents.Isolate Bases and Exponents: Isolate the bases and their exponents. Since the exponents are already isolated (60x on the left side and x on the right side), we can equate the bases to solve for A.Equate the Bases: Equate the bases. Since the exponents are multiples of each other, we can equate the bases as follows: 0.9^60 = ASolve for A: Solve for A. To find A, we simply take the 60th power of 0.9: A = 0.9^60Match the Solution: Match the solution to the given choices. We have found that A = 0.9^60, which matches choice (B).

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Find the value of
A that makes the following equation true for all values of
x.

0.9^(60 x)=A^(x)
Choose 1 answer:
(A)
A=0.9*60
(B)
A=0.9^(60)
(c)
A=(60)/(0.9)
(D)
A=60^(0.9)

Find the value of $A$ that makes the following equation true for all values of $x$ . $\newline$ $0.9^{60 x}=A^{x}$ $\newline$ Choose $1$ answer: $\newline$ (A) $A=0.9 \cdot 60$ $\newline$ (B) $A=0.9^{60}$ $\newline$ (C) $A=\frac{60}{0.9}$ $\newline$ (D) $A=60^{0.9}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. Find the value of

A

that makes the following equation true for all values of

x

\newline

0.9^{60 x}=A^{x}

\newline

Choose

1

answer:

\newline

(A)

A=0.9 \cdot 60

\newline

(B)

A=0.9^{60}

\newline

(C)

A=\frac{60}{0.9}

\newline

(D)

A=60^{0.9}

Understand and Identify Bases: Understand the equation and identify the bases. $\newline$ We are given the equation $0.9^{60x} = A^{x}$ . We need to find the value of $A$ such that this equation holds true for all $x$ . To do this, we need to compare the bases of the exponents.
Isolate Bases and Exponents: Isolate the bases and their exponents. Since the exponents are already isolated ( $60x$ on the left side and $x$ on the right side), we can equate the bases to solve for $A$ .
Equate the Bases: Equate the bases. $\newline$ Since the exponents are multiples of each other, we can equate the bases as follows: $\newline$ $0.9^{60} = A$
Solve for A: Solve for A. $\newline$ To find $A$ , we simply take the $60$ th power of $0.9$ : $\newline$ $A = 0.9^{60}$
Match the Solution: Match the solution to the given choices. $\newline$ We have found that $A = 0.9^{60}$ , which matches choice $(B)$ .