Question 1187605
**a) Determining the function V(t):**

To find the function V(t) that represents the value of the fund *t* years after 1997, we need to integrate the growth rate function V'(t) = r(t).

∫V'(t) dt = ∫200e^(0.04t) dt

V(t) = (200/0.04)e^(0.04t) + C

V(t) = 5000e^(0.04t) + C

We know that in 1997 (t=0), the value of the fund is $1,000,000.  We can use this information to find the constant of integration, C.

1,000,000 = 5000e^(0.04*0) + C

1,000,000 = 5000 + C

C = 995,000

Therefore, the function representing the value of the fund *t* years after 1997 is:

V(t) = 5000e^(0.04t) + 995,000

**b) Determining the value of the fund in 2007:**

The year 2007 is 10 years after 1997, so we need to find V(10):

V(10) = 5000e^(0.04*10) + 995,000

V(10) = 5000e^(0.4) + 995,000

V(10) ≈ 5000 * 1.4918 + 995,000

V(10) ≈ 7459 + 995,000

V(10) ≈ 1,002,459

Therefore, the value of the fund in 2007 is approximately $1,002,459.