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

1.55 minutes = 1.55×60 = 93 seconds

Step2: Use continuous - growth formula

The formula for continuous growth is $A = Pe^{rt}$, where $P$ is the initial amount, $r$ is the growth rate, and $t$ is the time. Here, $P = 200$, $r=0.04$, and $t = 93$. $A=200\times e^{0.04\times93}$

Step3: Calculate the exponent

$0.04\times93 = 3.72$

Step4: Calculate the value of $e^{3.72}$

Using a calculator, $e^{3.72}\approx41.2997$

Step5: Calculate the final amount

$A = 200\times41.2997=8259.94$

Answer:

8259.94