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Exponential and Logartihmic Functions Essay

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Unit 5: Exponential and Logarithmic Functions Essay Exponential Function Exponential Functions: An exponential equation is a type of transcendental equation, or equation that can be solved for one factor in terms of another. An exponential function f with base a is denoted by f (x) = ax, where a is greater than 0, a can not equal 1, and x is any real number. The base 1 is excluded because 1 to any power yields 1. For example, 1 to the fourth power is 1×1×1×1, which equals 1. That is a constant function which is not exponential, so 1 is not allowed to be the base of an exponential equation. Otherwise, the base of a can be any number that is greater than 0 and isn’t 1, and x can be any real number. The equation for the parent …show more content…

The equation for it is offered below: P = principal amount (the initial amount you borrow or deposit) r = annual rate of interest (as a decimal, for example, 24% would be 0.24) t = number of years the amount is deposited or borrowed for. A = amount of money accumulated after n years, including interest. n = number of times the interest is compounded per year Continuously compounding interest is like compounding interest where the rate is applied to a larger amount, but the compounding period is infinitely small, causing it to continuously compound and follow an exponential curve. The final amount is expressed as the amount after t years of continuous compounding on a given principle. The equation for it is offered below: P = principal amount (initial investment) r = annual interest rate (as a decimal) t = number of years A = amount after time t Wells Fargo offers an interest rate for a savings account with a compounding interest of 6%, compounding twice a year. They also offer another savings account with continuously compounding interest of 3%. If you invest $1,000 into either bank for two years, which one will yield more money? Compounding Interest * Original Equation for Compounding Interest * Plug in the value for rate, 6% or 0.06, the number of times compounded, 2, the initial value, $1,000, and the time, which is 2 years. * Simplify * ←Answer

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