### Instruction: The doctor has told Cal O'Ree that during his ten weeks of working out at the gym, he can expect each week's weight loss to be $1\%$ of his weight at the end of the previous week. His weight at the beginning of the workouts is $244$ pounds. How many pounds does he expect to weigh at the end of the ten weeks? Express your answer to the nearest whole number.### Response: This problem involves exponential decay, since each week's weight loss is a constant percentage of the previous week's weight.
To model this situation, I can use an equation of the form $w(t) = w_0(1-r)^t$, where $w(t)$ is the weight at time $t$, $w_0$ is the initial weight, $r$ is the rate of decay, and $t$ is the time in weeks.
In this case, $w_0 = 244$, $r = 0.01$, and $t = 10$.
Plugging these values into the equation, I get $w(10) = 244(1-0.01)^{10}$.
To simplify this expression, I can use the exponent rules and the order of operations.
First, I can rewrite $(1-0.01)^{10}$ as $(0.99)^{10}$.
Then, I can use a calculator or the binomial theorem to find that $(0.99)^{10} \approx 0.904382$.
Multiplying this by $244$, I get $w(10) \approx 220.85$.
Rounding to the nearest whole number, I get $221$.
Therefore, Cal O'Ree expects to weigh $221$ pounds at the end of the ten weeks.