Final answer:
To find the function g(t) = abⁿt, we need to solve for the values of a, b, and n. We are given two sets of values for g(t). Using these values, we can create two equations and solve them simultaneously to find the values of a, b, and n.
Step-by-step explanation:
To find the function g(t) = abⁿt, we need to solve for the values of a, b, and n. We are given two sets of values for g(t). Using these values, we can create two equations and solve them simultaneously to find the values of a, b, and n.
Using the provided values of g(20) = 77 and g(50) = 20, we can substitute these values into the function and create the following equations:
77 = abⁿ(20) and 20 = abⁿ(50).
Simplifying these equations, we get:
abⁿ = 77/20 = 3.85 and abⁿ = 20/50 = 0.4.
Now, we can divide these two equations to eliminate abⁿ:
(abⁿ)/(abⁿ) = (3.85)/(0.4).
Solving this equation, we find that n = log(3.85/0.4) / log(20/50).
Substituting the value of n back into one of the original equations, we can solve for a and b.
Once we have the values of a, b, and n, we can substitute them back into the function g(t) = abⁿt to find the final equation.