The value of an investment of $4,000 after t years in an account for which the interest rate 100r% is compounded continuously is given by the function dollars. Write the partial derivative

Question

The value  of an investment of $4,000 after t years in an account for which the interest rate 100r% is compounded continuously is given by the function  dollars. Write the partial derivative

Quizplus · Accepted Answer

To find the partial derivative with respect to r, we differentiate the expression inside the bracket and multiply by the derivative of the exponent:
d/dx [4000e^(t*x)] = 4000t*e^(t*x)
We replace x with 0.01r to get:
d/dx [4000e^(t*0.01r)] = 40te^(t*0.01r)
Therefore, the partial derivative with respect to r is 40te^(t*0.01r), which is equivalent to choice (B).

The Value of an Investment of $4,000 After T