Question

algebra: concepts and connections - plc
analyzing the meaning of expressions
which expressions represent exponential decay? choose three correct answers.
53(1.75)(0.3)^x
700(0.9)^x
18 - 3y
90(1.2)^t
2x^2 + 9
300(2.4)(1.2)^y
900(0.05)^t

Explanation:

Step1: Define exponential decay form

An exponential decay expression follows the form $A(b)^x$, where $0 < b < 1$, and $A$ is a positive constant.

Step2: Evaluate each expression

• $53(1.75)(0.3)^x$: The base of the exponent is $0.3$, which is between 0 and 1. This is exponential decay.
• $700(0.9)^x$: The base of the exponent is $0.9$, which is between 0 and 1. This is exponential decay.
• $18-3y$: This is a linear expression, not exponential.
• $90(1.2)^t$: The base $1.2 > 1$, this is exponential growth.
• $2x^2+9$: This is a quadratic expression, not exponential.
• $300(2.4)(1.2)^y$: The base $1.2 > 1$, this is exponential growth.
• $900(0.05)^t$: The base of the exponent is $0.05$, which is between 0 and 1. This is exponential decay.

Answer:

$53(1.75)(0.3)^x$, $700(0.9)^x$, $900(0.05)^t$