Infinite Series If you invest $2000 at the start of every year into an account earning 5% interest. Using the , we find that the value of the account at the end of the first 3 years is: Value at End of Year 1 = $2000 x 1.051= $2100 at End of Year 2 = $2000 x 1.051 + $2000 x 1.052 = $4305 at End of Year 3 = $2000 x 1.051 + $2000 x 1.052 + $2000 x 1.053 = $6620.25 If you look closely, you’ll see that this sequence of expressions for the value of the investment at the end of each year form a mathematical series where each term is the amount of money invested each year—$2000—multiplied by the interest rate raised to . Inverse Function If you wanted to know how many years it will take for your $2000.00 to double with a 5% interest then you would use logarithm(inverse of exponential) to answer this question for example 2 = How many times do you need to multiply 1.05 by itself to get 2? You can take log on both sides to answer this question Log2/log1.05 = t Pictorial Exponential function (Coordinate Plane) Inverse Exponential function Transformed Exponential function Rule/Function Geometric Sequence Recursive is the nth term of the sequence is the previous term of the nth term of the sequence is the common n is the term number Explicit
Infinite Series If you invest $2000 at the start of every year into an account earning 5% interest. Using the , we find that the value of the account at the end of the first 3 years is: Value at End of Year 1 = $2000 x 1.051= $2100 at End of Year 2 = $2000 x 1.051 + $2000 x 1.052 = $4305 at End of Year 3 = $2000 x 1.051 + $2000 x 1.052 + $2000 x 1.053 = $6620.25 If you look closely, you’ll see that this sequence of expressions for the value of the investment at the end of each year form a mathematical series where each term is the amount of money invested each year—$2000—multiplied by the interest rate raised to . Inverse Function If you wanted to know how many years it will take for your $2000.00 to double with a 5% interest then you would use logarithm(inverse of exponential) to answer this question for example 2 = How many times do you need to multiply 1.05 by itself to get 2? You can take log on both sides to answer this question Log2/log1.05 = t Pictorial (Coordinate Plane) Exponential function Inverse Exponential function Transformed Exponential function Rule/Function Geometric Sequence Recursive is the nth term of the sequence is the previous term of the nth term of the sequence is the common n is the term number Explicit
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