the value, v, of kalanis stock investments over a time period, x, can be determined using the equation v =…

the value, v, of kalanis stock investments over a time period, x, can be determined using the equation v = 750(0.80)^-x. what is the rate of increase or decrease associated with this account? 20% decrease 20% increase 25% decrease 25% increase

the value, v, of kalanis stock investments over a time period, x, can be determined using the equation v = 750(0.80)^-x. what is the rate of increase or decrease associated with this account? 20% decrease 20% increase 25% decrease 25% increase

Answer

Explanation:

Step1: Rewrite the equation

The general form of an exponential - growth or decay function is $V = a(b)^x$. Given $V = 750(0.80)^{-x}$, we can rewrite it using the negative - exponent rule $a^{-n}=\frac{1}{a^{n}}$. So, $V = 750(0.80)^{-x}=750(\frac{1}{0.80})^{x}=750(1.25)^{x}$.

Step2: Identify the growth factor

In the exponential function $V = a(b)^x$, if $b>1$, it is a growth function, and the rate of increase $r$ is given by $b = 1 + r$. Here, $b = 1.25$.

Step3: Calculate the rate of increase

Set $1 + r=1.25$. Solving for $r$, we subtract 1 from both sides: $r=1.25 - 1=0.25$. To convert $r$ to a percentage, we multiply by 100. So, $r = 25%$.

Answer:

25% increase