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Clever 21:08 Wed Sep 18

51%
ixl.com
Algebra 2
Z.9 Exponential growth and decay: word proble
You have prizes to reveall Go to your game board.
Video
Questions
answered
In Booneville, the use of landlines has been declining at a rate of 
20% every year. If there are 25,300 landlines this year, how many will there be in 5 years?
29
If necessary, round your answer to the nearest whole number.
Time
elapsed
00
31
52
HR
MIN
SEC
SmartScore
out of 100
65

Clever 2121:0808 Wed Sep 1818\newline51% 51 \% \newlineixl.com\newlineAlgebra 22\newlineZ.99 Exponential growth and decay: word proble\newlineYou have prizes to reveall Go to your game board.\newlineVideo\newlineQuestions\newlineanswered\newlineIn Booneville, the use of landlines has been declining at a rate of 20% 20 \% every year. If there are 2525,300300 landlines this year, how many will there be in 55 years?\newline2929\newlineIf necessary, round your answer to the nearest whole number.\newlineTime\newlineelapsed\newline0000\newline3131\newline5252\newlineHR\newlineMIN\newlineSEC\newlineSmartScore\newlineout of 100100\newline6565

Full solution

Q. Clever 2121:0808 Wed Sep 1818\newline51% 51 \% \newlineixl.com\newlineAlgebra 22\newlineZ.99 Exponential growth and decay: word proble\newlineYou have prizes to reveall Go to your game board.\newlineVideo\newlineQuestions\newlineanswered\newlineIn Booneville, the use of landlines has been declining at a rate of 20% 20 \% every year. If there are 2525,300300 landlines this year, how many will there be in 55 years?\newline2929\newlineIf necessary, round your answer to the nearest whole number.\newlineTime\newlineelapsed\newline0000\newline3131\newline5252\newlineHR\newlineMIN\newlineSEC\newlineSmartScore\newlineout of 100100\newline6565
  1. Identify Initial Data: Identify the initial number of landlines and the annual decline rate. Initial landlines = 25,30025,300 Annual decline rate = 20\text{%} = 0.20
  2. Calculate Remaining Percentage: Calculate the remaining percentage of landlines each year. Remaining percentage = 100%20%=80%=0.80100\% - 20\% = 80\% = 0.80
  3. Use Exponential Decay Formula: Use the exponential decay formula to find the number of landlines after 55 years. Formula: Final amount = Initial amount ×\times (remaining percentage)number of years^{\text{number of years}}
  4. Plug in Values: Plug in the values and calculate. Final amount = 25,300×(0.80)525,300 \times (0.80)^5
  5. Calculate Exponential Value: Calculate (0.80)5(0.80)^5. (0.80)5=0.32768(0.80)^5 = 0.32768
  6. Multiply Initial Amount: Multiply the initial amount by the result from Step 55. Final amount = 25,300×0.32768=8,287.10425,300 \times 0.32768 = 8,287.104
  7. Round Final Amount: Round the final amount to the nearest whole number. Final amount 8,287\approx 8,287

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