Use the compound interest equation B(t)=800(1.0001)^365t to answer the questions.
A: What is the the equation rewritten in the form B(t)=P(1+r/n)^nt? (Assume n=365.)
B: What is the interest rate, r, as a percentage?
To rewrite the equation B(t)=800(1.0001)^365t in the form B(t)=P(1+r/n)^nt, we need to identify the corresponding values for P, r, and n.
In the given equation B(t)=800(1.0001)^365t, we can see that 800 represents the principal amount (P) and 365 represents the number of times interest is compounded in a year (n).
So, we have P = 800 and n = 365.
Now, let's identify the value of r. In the compound interest formula, r represents the interest rate.
To find r as a percentage, we can rearrange the equation and solve for r.
B(t) = P(1+r/n)^nt
800(1.0001)^365t = 800(1 + r/365)^(365t)
Dividing both sides by 800:
(1.0001)^365t = 1 + r/365
Subtracting 1 from both sides:
(1.0001)^365t - 1 = r/365
Multiplying both sides by 365:
365 * [(1.0001)^365t - 1] = r
Now, we can calculate the value of r.