question a quantity with an initial value of 2300 grows continuously at a rate of 45% per minute. what is…

question a quantity with an initial value of 2300 grows continuously at a rate of 45% per minute. what is the value of the quantity after 0.2 hours, to the nearest hundredth? answer attempt 1 out of 2 submit answer

question a quantity with an initial value of 2300 grows continuously at a rate of 45% per minute. what is the value of the quantity after 0.2 hours, to the nearest hundredth? answer attempt 1 out of 2 submit answer

Answer

Explanation:

Step1: Convert time to minutes

Since 1 hour = 60 minutes, 0.2 hours = 0.2×60 = 12 minutes.

Step2: Use continuous - growth formula

The formula for continuous growth is $A = A_0e^{rt}$, where $A_0$ is the initial value, $r$ is the growth rate (as a decimal), and $t$ is the time. Here, $A_0 = 2300$, $r=0.45$, and $t = 12$. So $A=2300\times e^{0.45\times12}$.

Step3: Calculate the exponent

$0.45\times12 = 5.4$. So $A = 2300\times e^{5.4}$.

Step4: Find the value of $e^{5.4}$

Using a calculator, $e^{5.4}\approx 221.4064$.

Step5: Calculate the final value of $A$

$A=2300\times221.4064 = 509234.72$.

Answer:

$509234.72$