Question

algebra 1b - standard (15261)
ential decay functions
when initially observed, a lake measured 79 feet in depth. due to the rate of evaporation exceeding the rate of rainfall in the region, the depth of the lake is projected to decrease exponentially at a rate of 3% each year.
write an exponential function to model the projected depth of the lake. let the variable $x$ represent the number of years since the depth of the lake was initially measured. let $f(x)$ represent the depth, in feet, of the lake after $x$ years.
enter your answer in the box.
$f(x) = \square$

Explanation:

Step1: Recall exponential decay formula

The general form of an exponential decay function is $f(x) = a(1-r)^x$, where $a$ is the initial value, $r$ is the decay rate, and $x$ is time.

Step2: Identify given values

Initial depth $a = 79$ feet, decay rate $r = 3\% = 0.03$.

Step3: Substitute values into formula

Substitute $a=79$ and $r=0.03$ into the formula:
$f(x) = 79(1-0.03)^x = 79(0.97)^x$

Answer:

$f(x)=79(0.97)^x$