determine whether the function represents exponential growth or decay. write the base in terms of the rate…

determine whether the function represents exponential growth or decay. write the base in terms of the rate of growth or decay, identify r, and interpret the rate of growth or decay. \n$y=12,100\\left(\\frac{3}{10}\\right)^x$\n\nthe function $y=12,100\\left(\\frac{3}{10}\\right)^x$ represents exponential $square$ rewriting the base in terms of the rate of growth or decay results in the function $y=12,100(\\square)^x$\nin this function, $r=\\square$ which indicates that the value of y $square$ by $square$% each time period.

determine whether the function represents exponential growth or decay. write the base in terms of the rate of growth or decay, identify r, and interpret the rate of growth or decay. \n$y=12,100\\left(\\frac{3}{10}\\right)^x$\n\nthe function $y=12,100\\left(\\frac{3}{10}\\right)^x$ represents exponential $square$ rewriting the base in terms of the rate of growth or decay results in the function $y=12,100(\\square)^x$\nin this function, $r=\\square$ which indicates that the value of y $square$ by $square$% each time period.

Answer

Explanation:

Step1: Identify growth/decay type

An exponential function has the form $y = a(b)^x$. If $0 < b < 1$, it is decay. Here, $b = \frac{3}{10} = 0.3$, which is between 0 and 1.

Step2: Rewrite base for decay rate

For decay, $b = 1 - r$. Rearrange to solve for $r$: $r = 1 - b = 1 - \frac{3}{10} = \frac{7}{10} = 0.7$ Rewrite the function using $1 - r$: $y = 12,100(1 - 0.7)^x$

Step3: Interpret the rate

$r = 0.7$ means the value decreases by $0.7 \times 100 = 70%$ per period.

Answer:

The function $y = 12,100\left(\frac{3}{10}\right)^x$ represents exponential decay. Rewriting the base in terms of the rate of growth or decay results in the function $y = 12,100(1 - 0.7)^x$ In this function, $r = 0.7$ which indicates that the value of $y$ decreases by $\boldsymbol{70}$% each time period.