jason is going to invest $1,900 and leave it in an account for 6 years. assuming the interest is compounded…

Explanation:

Step1: Recall continuous - compounding formula

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate, and $t$ is the time in years. We are given that $P=$1900$, $A = $2400$, and $t = 6$ years. Substitute these values into the formula: $2400=1900e^{6r}$.

Step2: Isolate the exponential term

Divide both sides of the equation by 1900: $\frac{2400}{1900}=e^{6r}$, which simplifies to $\frac{24}{19}=e^{6r}$.

Step3: Take the natural logarithm of both sides

$\ln(\frac{24}{19})=\ln(e^{6r})$. Since $\ln(e^{x}) = x$, the right - hand side simplifies to $6r$. So, $\ln(\frac{24}{19}) = 6r$.

Step4: Solve for $r$

First, calculate $\ln(\frac{24}{19})\approx\ln(1.26316)\approx0.2337$. Then, $r=\frac{\ln(\frac{24}{19})}{6}$. Substitute the value of $\ln(\frac{24}{19})$: $r=\frac{0.2337}{6}=0.03895$.

Step5: Convert to percentage and round

To convert $r$ to a percentage, multiply by 100: $r = 3.895%$. Rounding to the nearest hundredth of a percent, $r\approx3.90%$.

Answer:

$3.90%$