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$y=13,300\\left(\\frac{3}{4}\\right)^x$\nthe function $y=13,300\\left(\\frac{3}{4}\\right)^x$ represents exponential $\\boldsymbol{\\blacktriangledown}$ rewriting the base in terms of the rate of growth or decay results in the function $y=13,300(\\square)^x$\nin this function, $r=\\square$ which indicates that the value of y $\\boldsymbol{\\blacktriangledown}$ by $\\square\\%$ each time period.\nhelp me solve this view an example get more help ▸\nclear all

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$y=13,300\\left(\\frac{3}{4}\\right)^x$\nthe function $y=13,300\\left(\\frac{3}{4}\\right)^x$ represents exponential $\\boldsymbol{\\blacktriangledown}$ rewriting the base in terms of the rate of growth or decay results in the function $y=13,300(\\square)^x$\nin this function, $r=\\square$ which indicates that the value of y $\\boldsymbol{\\blacktriangledown}$ by $\\square\\%$ each time period.\nhelp me solve this view an example get more help ▸\nclear all

Answer

Explanation:

Step1: Identify base type

The function is $y=13,300\left(\frac{3}{4}\right)^x$. Since $\frac{3}{4}=0.75<1$, this is exponential decay.

Step2: Rewrite base for decay rate

The standard decay form is $y=a(1-r)^x$. Set $1-r=0.75$.

Step3: Solve for decay rate $r$

$r=1-0.75=0.25$, or $25%$.

Answer:

The function represents exponential decay. Rewriting the base in terms of the rate of decay results in the function $y=13,300(0.75)^x$. In this function, $r=0.25$ which indicates that the value of $y$ decreases by $25%$ each time period.