Pg. 255/268 Homework• Pg. 277 #32 – 40 all

Pg. 310 #1, 2, 7, 41 – 48

• #6 left 2, up 4 #14 Graph• #24 x = #28 x = 6• #35 Graph #51 r = 6.35, h = 9, V = 380• #1 Graph #3 a) dec b) inc c) dec• #5 Down 4 #6 Stretch 3• #7 Right 3 #8 Reflect x and y axes• #9 Left 1, Up 7 #15 a = c

7 1 78 2 2

5.1 Exponential Functions

Life Span Problems• The formula for Life Span

problems is similar to the continuous growth/decay equation using e.

• Population:

• Life Span:

• Suppose the half-life of a certain radioactive substance is 20 days and there are 5g present initially. – Write an equation to

represent the situation.– Draw a complete graph.– Find when there will be less

than 1g of the substance remaining.

𝑦=𝑃 (𝑎 )𝑡𝑑

𝑆=𝑃 𝑒𝑟𝑡

5.2 Simple and Compound Interest

Compound Interest• Compound Interest is when

financial institutions pay interest on the interest. (Yay… more money!)

• Suppose P dollars are invested at an interest rate r, then the compound interest formula for the total amount S after n interest periods is:

Example• Sally invests $500 at 7%

interest compounded annually. Find the value of the investment after 10 years.

• How much should Sally invested at 6.25% compounded semi-annually in order to have an investment of $1,500 after 5 years?

𝑆=𝑃 (1+ 𝑟𝑛 )𝑛𝑡

5.2 Simple and Compound Interest

Compound Interest• Sally invests $1000 at 8%.

Find the value of the investment after one year when it is compounded– Annually– Quarterly– Monthly– Weekly– Daily– Hourly– Continuously

Continuous Interest• If P dollars are invested at

an APR, r, (in decimal form) and compounded continuously, then the value of the investment after t years is given by:

S = Pert