High School

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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

[tex] y = 3700(0.97)^x [/tex]

1. Is it growth or decay?
2. What is the percentage rate of increase or decrease?

Answer :

To analyze the function

[tex]$$
y = 3700(0.97)^x,
$$[/tex]

we first look at the base of the exponent, which is [tex]$0.97$[/tex]. Since [tex]$0.97$[/tex] is less than [tex]$1$[/tex], the function represents a decay rather than growth.

Next, to determine the percentage rate of decrease, we subtract the base from [tex]$1$[/tex] and then multiply by [tex]$100\%$[/tex]:

[tex]$$
\text{Percentage decrease} = (1 - 0.97) \times 100\% = 0.03 \times 100\% = 3\%.
$$[/tex]

Thus, the function represents decay with a [tex]$3\%$[/tex] decrease per unit increase in [tex]$x$[/tex].

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