Let be any real number and let be a differentiable function of n u The Power Rule for Real Exponents gives. x. [xn ] = . d dx [un ] = [du/dx] . d dx Applications of Exponential Functions (Pages What you should How to use exponential Complete the following limit statement: functions to model compound interest and x x lim 1 + = lim + 1 exponential growth x = . e x x Let be the amount deposited, the number of years, the P t A balance after years, and the annual interest rate (in decimal t r form), and the number of compounding per year. Complete the n following compound interest formulas: Compounded per year: = + n A P(1 r/n)nt Compounded continuously: = A Pert Example 2: Find the amount in an account after 10 years if $6000 is invested at an interest rate of 7%, compounded monthly. compounded continuously. (a) $12,057.97 (b) $12,082.52
Let n be any real number and let u be a differentiable function of x. The Power Rule for Real Exponents gives. d [xn ] = . dx d [un ] = [du/dx] . dx Applications of Exponential Functions (Pages Complete the following limit statement: x x What you should How to use exponential functions to model compound interest and lim + 1 = lim x + 1 = e . exponential growth x x Let P be the amount deposited, t the number of years, A the balance after t years, and r the annual interest rate (in decimal form), and n the number of compounding per year. Complete the following compound interest formulas: Compounded n per year: A = P(1 + r/n)nt Compounded continuously: A = Pert Example 2: Find the amount in an account after 10 years if $6000 is invested at an interest rate of 7%, compounded monthly. compounded continuously. (a) $12,057.97 (b) $12,082.52
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