Warm up honors algebra 2 3/7/19 Find the inverse function: 1. 𝑦=2𝑥+5 3. 𝑦=3 ln 𝑥+1 2. 𝑓 𝑥 =2 𝑥+1 4. 𝑓 𝑥 =4 5 𝑥

Find the inverse function 𝑓 𝑥 =5 1 5 𝑥 𝑥=5 1 5 𝑦 𝑥 5 = 1 5 𝑦 𝑙𝑜𝑔 1 5 𝑥 5 =𝑦= 𝑓 −1 (𝑥)

Which equations are true for all values of x? Select all that apply. B) ( 3 𝑥 ) 2 = (3 2 ) 𝑥 C) 27 𝑥 = ( 3 𝑥 ) 3 D) 3 𝑥+2 =9( 3 𝑥 ) E) 9 𝑥+2 = 3 2𝑥+4

Same exponential bases What happens if exponential terms have the same bases? 2 (2𝑥) = 2 (𝑥+4) 2𝑥=𝑥+4 𝑥=4

Solve 8 𝑥 = 2 𝑥+6 8 𝑥  (2 3 ) 𝑥  2 3𝑥 2 3𝑥 = 2 𝑥+6 3𝑥=𝑥+6 2𝑥=6 𝑥=3 Rewrite each side so that they have the same base 8 𝑥  (2 3 ) 𝑥  2 3𝑥 2 3𝑥 = 2 𝑥+6 3𝑥=𝑥+6 2𝑥=6 𝑥=3

16 𝑥  (4 2 ) 𝑥  4 2𝑥 4 4𝑥+1 =4 2𝑥 4𝑥+1=2𝑥 1=−2𝑥 𝑥=− 1 2 Solve 4 4𝑥+1 = 16 𝑥 16 𝑥  (4 2 ) 𝑥  4 2𝑥 4 4𝑥+1 =4 2𝑥 4𝑥+1=2𝑥 1=−2𝑥 𝑥=− 1 2

144 2𝑥  ( 12 2 ) 2𝑥  12 4𝑥 12 4𝑥 = 12 6𝑥−1 4𝑥=6𝑥−1 −2𝑥=−1 𝑥= 1 2 Solve 144 2𝑥 = 12 6𝑥−1 144 2𝑥  ( 12 2 ) 2𝑥  12 4𝑥 12 4𝑥 = 12 6𝑥−1 4𝑥=6𝑥−1 −2𝑥=−1 𝑥= 1 2

25 5𝑥  (5 2 ) 5𝑥  5 10𝑥 5 𝑥+3 = 5 10𝑥 𝑥+3=10𝑥 3=9𝑥 𝑥=1/3 Solve 5 𝑥+3 = 25 5𝑥 25 5𝑥  (5 2 ) 5𝑥  5 10𝑥 5 𝑥+3 = 5 10𝑥 𝑥+3=10𝑥 3=9𝑥 𝑥=1/3

Solve 36 −3𝑥 = 6 2𝑥−1 36 −3𝑥  (6 2 ) −3𝑥  6 −6𝑥 6 −6𝑥 = 6 2𝑥−1 36 −3𝑥  (6 2 ) −3𝑥  6 −6𝑥 6 −6𝑥 = 6 2𝑥−1 −6𝑥=2𝑥−1 −8𝑥=−1 𝑥=1/8

Solve −49 −𝑥 = 7 3𝑥−1 −49 −𝑥  −( 7 2 ) −𝑥  −( 7 −2𝑥 ) −(7) −2𝑥 = 7 3𝑥−1 − −2𝑥 =3𝑥−1 2𝑥=3𝑥−1 −𝑥=−1 𝑥=1

A bank pays depositors a 2% interest rate compounded semi-annually A bank pays depositors a 2% interest rate compounded semi-annually. Let P represent an initial deposit, and t represent the number of years that the deposit is in the bank. The expression 𝑃 1+ 0.02 2 2𝑡 can be used to determine the account balance after t years. Which expression accurately reflects the annual interest rate? A) 𝑃 1.01 𝑡 B) 𝑃 1.21 𝑡 C) 𝑃 1.0201 𝑡 D) 𝑃 1.0404 𝑡

Solve for n 1. 10 𝑛 =4.305 2. 10 𝑛 =0.316 3. 10 𝑛 =14,521 4. 10 𝑛 =483.059 log 4.305 =𝑛 log 0.316 =𝑛 log 14,521 =𝑛 log 483.059 =𝑛 𝑛=.634 𝑛=−.5003 𝑛=4.162 𝑛=2.684