PAP Algebra 2 – Exponential and logarithmic functions part 1 RETEACH/REVIEW highest water level before the decrease started was 1. Solve the following equation then, round to the 300 ft, what was the level at the end of 9 weeks? nearest tenth. 9 5 2
Round to the nearest foot.  Over the past several months, the water level of a  Solve the following equation. 7 2 5
lake has been decreasing by 1.25% each week. If the  Solve the following equation then, round the highest water level before the decrease started was answer to three decimal places. 13 1 3
425 ft, what was the level at the end of 10 weeks?  Solve the following equation then, round to the Round to the nearest foot. nearest hundredth. 24
8 4
 Over the past several months, the water level of a lake has been decreasing by 2.5% each week. If the 2. Solve the equation 6 ln(3x) = 8. Round the answer to highest water level before the decrease started was three decimal places. 712 ft, what was the level at the end of 6 weeks? Round to the nearest foot.  Solve the equation 4 ln(5x) = 5. Round the answer to one decimal place. 5. Susan has $7125 in her home safe. She takes of this  Solve the equation ‐7 ln(2x) = ‐14. Round the answer to two decimal places. amount and invests it in an account that earns 3.75%  Solve the equation 3 ln(4x) = 17. Round the answer interest, compounded continuously. She takes to three decimal places. another of the money from the safe and invests it in an account that earns 4.25% interest, compounded 3. Given the function f(x)= ??????, which of one the annually. She also leaves of the money in the safe. If following statements is not true? there are no withdraws from the safe or either of the accounts after she makes her investments what is the  Given the function log
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3 1
total amount Susan will have in 3 years? o Find f  x   Amanda has $19,145 in her home safe. She takes o Find f(8), f(4), f‐1(8) and f‐1(4) of this amount and invests it in an account that o Find the asymptote for f(x) and f‐1(x) ‐1
earns 2.75% interest, compounded continuously. o Are f(x) and f (x) increasing or She takes another of the money from the safe and decreasing functions?  Given the function 10
8 invests it in an account that earns 3.25% interest, 1
compounded annually. She also leaves of the o Find f  x  money in the safe. If there are no withdraws from o Find f(3), f(2), f‐1(9) and f‐1(18) ‐1
the safe or either of the accounts after she makes o Find the asymptote for f(x) and f (x) ‐1
her investments what is the total amount Amanda o Are f(x) and f (x) increasing or will have in 5 years? decreasing functions?  Christy has $10,752.50 in her home safe. She takes  Given the function ln
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7 1
of this amount and invests it in an account that o Find f  x  earns 2. 5% interest, compounded continuously. o Find f(‐2), f(‐7), f‐1(‐2) and f‐1(‐7) She takes another of the money from the safe and o Find the asymptote for f(x) and f‐1(x) ‐1
invests it in an account that earns 4. 5% interest, o Are f(x) and f (x) increasing or decreasing functions? compounded annually. She also leaves of the money in the safe. If there are no withdraws from 4. Over the past several months, the water level of a the safe or either of the accounts after she makes lake has been decreasing by 1.5% each week. If the her investments what is the total amount Amanda highest water level before the decrease started was will have in 5 years? 597 ft, what was the level at the end of 5 weeks? Round to the nearest foot. 6. Juan has $5,000 and invests it in an account that  Over the past several months, the water level of a earns 2. 5% interest, compounded annually. Luis has lake has been decreasing by .95% each week. If the $4,500 and invests it in an account that earns 3. 5% 9. Write a function that has the same x intercept value as the y intercept value for the function ln
3
7 10.
Solve for g ln
3
7 8 11.
Solve for h 3∙
12. An initial deposit of $400 is placed in a bank account and left to grow, with interest compounded continuously. If the account balance is $449 after 1 year and 6 months, what will it be after 3 years? Round your answer to the nearest cent. 13. An initial deposit of $500 is placed in a bank account and left to grow, with interest compounded continuously. If the account balance is $525 after 2 years and 9 months, what will it be after 6 years? Round your answer to the nearest cent. interest, compounded continuously. William has $6,000 that he keeps in a safe at home. If no one makes any deposits or withdraws from their safe or account who has the most money in 6 years? In 11 years? 7. Keiston, Eric and Deon all invest money on the same day. Keiston invests $10,000 in the stock market and ends up losing 5% each year. Eric invests $6,000 into an account and earns 4.5% interest compounded continuously. Deon invests $80 in a up and coming company. Deon doubles his money each year as the company does really well. If not additional deposits or withdraws are made who has the most money after 5 years? After 6 years? After 7 years? 8. Write a function that has the same y intercept value as the x intercept value for the function .2 ∙ 10
8 14.
Given the function f  x  represented in table below, graph f
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x ‐1 f  x 6 
9
4
5 
5
2
4 ‐3 ‐5 3 2  x