Ch 5 Review

5.1- Interest formulas Simple Interest: A = P + P x r x n Arithmetic sequences Linear functions A loan for $50,000 accrues 5% interest per year F(n)= 50000 + 50000 x 0.05 x n Compound Interest: 𝐴=𝑃 (1+𝑟) 𝑛 Geometic sequences Exponential functions A loan for $50,000 accrues 5% compound interest per year F(n)=50000 (1+0.05) 𝑛 n F(n) 50000 1 52500 2 55000 3 57500 4 60000 n F(n) 50000 1 52500 2 55125 3 57881.25 4 60775.31 Ex: How much do you have after 3 years with a savings account with $120,000 that earns 2%compounded interest? Ex: How much do you pay after 6 years for an $80,000 loan with a 4.125% simple interest rate?

5.2 Exponential Functions: 𝑦=𝑎∗ 𝑏 𝑥 a is the y-intercept because the y- intercept is where x = 0 𝑦=𝑎∗ 𝑏 0 𝑦=𝑎∗1 𝑦=𝑎 Exponential functions have horizontal asymptotes – a horizontal line that the function gets very close to but never actually crosses. The HA here is y = 0 x Y 5 1 10 2 20 3 40 We can find the exponential function given a table or graph. A = 5 because it is the y-intercept so we know 𝑦=5∗ 𝑏 𝑥 Then we can use any other point to find b: Using the point (1, 10) plug in 1 for x and 10 for y 10=5∗ 𝑏 1 Now solve for b 2= 𝑏 1 so b = 2 The function is y=5∗ 2 𝑥

5.6- Solving Exponential equations Graphing: y = 3∗ 4 𝑥 a curve y = 48 a horizontal line The intersection point is the solution Given the equation 3∗ 4 𝑥 =48, solve for x Use the graph Or solve algebraically Algebraically: 1. Isolate the exponential term 3∗ 4 𝑥 =48 divide both sides by 3 4 𝑥 =16 2. Re-write each side as an exponential expression with the same base 4 𝑥 = 4 2 3. Set exponents equal to each other 𝑥=2 4. Solve for x if necessary 5. Check answer To find intersection on calculator Type functions into y= Hit 2nd, calc Choose #5 Enter, enter, enter Example: Use either method to solve 2∗ 5 𝑥−1 =250