peter is conducting a chemical experiment in a controlled environment. the initial temperature of the…

peter is conducting a chemical experiment in a controlled environment. the initial temperature of the chemical solution was 20°c. the temperature of the solution was 1.5 times the initial temperature after 3 minutes. the temperature of the solution continued to increase at this rate. this situation is graphed below. let x represent the number of minutes passed after the start of the experiment, and let f(x) represent the temperature of the solution. once the temperature reached 45°c, the experiment was stopped. over which interval did peter conduct the experiment? a. 0≤x≤3 b. 0≤x≤6 c. 0≤x≤2 d. 2≤x≤6

peter is conducting a chemical experiment in a controlled environment. the initial temperature of the chemical solution was 20°c. the temperature of the solution was 1.5 times the initial temperature after 3 minutes. the temperature of the solution continued to increase at this rate. this situation is graphed below. let x represent the number of minutes passed after the start of the experiment, and let f(x) represent the temperature of the solution. once the temperature reached 45°c, the experiment was stopped. over which interval did peter conduct the experiment? a. 0≤x≤3 b. 0≤x≤6 c. 0≤x≤2 d. 2≤x≤6

Answer

Explanation:

Step1: Find temperature after 3 minutes

Initial temperature $T_0 = 20^{\circ}C$. After 3 minutes, temperature $T_3=1.5\times20 = 30^{\circ}C$.

Step2: Analyze the growth pattern

The temperature is increasing exponentially. We know the experiment stops at $T = 45^{\circ}C$. Since the temperature at 3 minutes is $30^{\circ}C$ and it is increasing, and the experiment starts at $x = 0$ and ends when it reaches $45^{\circ}C$. By observing the growth trend, we can see that it will reach $45^{\circ}C$ after 3 minutes but before a long - time increase. We assume the exponential growth formula $T(x)=T_0\cdot a^{\frac{x}{t}}$ (where $T_0$ is initial temperature, $a$ is the growth factor, $x$ is time and $t$ is a time - related parameter). Here we can also estimate from the fact that from $20^{\circ}C$ to $30^{\circ}C$ in 3 minutes, and from $30^{\circ}C$ to $45^{\circ}C$ (a 1.5 - fold increase again) will also take about 3 minutes. So the experiment is conducted from $x = 0$ to $x=6$ minutes.

Answer:

B. $0\leq x\leq6$