Find a formula for the inverse of the following functions fx

Find a formula for the inverse of the following functions: f(x) = 3 squareroot x + 1/2 - 3 squareroot x g(x) = squareroot 6 - x^3/x^3 - 1 h(x) = log(x^2 - 5) m(x) = 3e^4x Consider the equations f(x) = x^2 + 4 g(x) =4x - 2, h(x) = 1/2x Generate and simplify f(g(x)) h(f(g(x)) Generate a formula for an exponential function that passes through the points (3, 18, 9) and (6, 510.3) Banks A, M, and C all offer an interest rate of 8% a year. Bank A compounds annually. Bank M compounds monthly. Bank C compounds continuously. 500 dollars is deposited in each bank. Find a formula for the balance B_A of the account after t years in Bank A. Find a formula for the balance B_M of the account after t years in Bank M. Find a formula for the balance B_C of the account after t years in Bank C. What is the effective annual rate at Bank M? How long would it take to achieve a balance of 550 dollars at Bank C?

Solution

solution:

problem 9

The formula for annual compound interest is A = P (1 + r/n) ^ nt:

Where:

A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for

now

a) for after t years balane will be

B=500(1+0.08/1)^t

=500(1.08)^t

b) for monthly interest rate n=12 hence

B=500(1+(0.08/12))^12t

B=500(1.0066)^12t

c) For continously compounded rate the formula for amount is

A=Pe^rt

where r= rate in decimal

t=time in years

hence

B=500e^0.08t

d) effective annual rate at bank M

= 0.08/12=0.0066per month

e) we have found formula

A=Pe^rt

550=500e^0.08t

0.08t=ln(550/500)

0.08t=0.095

t=1.191 years