a quantity with an initial value of 200 grows continuously at a rate of 4% per second. what is the value of…

Explanation:

Step1: Convert time to seconds

Since 1 minute = 60 seconds, 1.55 minutes = 1.55×60 = 93 seconds.

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, and $t$ is the time. Here, $A_0 = 200$, $r=0.04$ (4% expressed as a decimal), and $t = 93$. So $A=200e^{0.04\times93}$.

Step3: Calculate the value

First, calculate $0.04\times93 = 3.72$. Then, $e^{3.72}\approx41.291$. Multiply by 200: $A = 200\times41.291=8258.20$.

Answer:

8258.20