PLEASE, PLEASE HELP ME WITH THESE THREE QUESTIONS 1. The number of bacteria in a

Question

PLEASE, PLEASE HELP ME WITH THESE THREE QUESTIONS
1. The number of bacteria in a culture quadruples every 15 hours. How many times more bacteria are there after 30 hours than there are after 20 hours?

2. An investment of $100 doubles in value every 5 years. How long would it take to be worth $100,000?

3. The number of rolls of film sold last year was 3 million and is decreasing at a rate of 17% per year. The number of digital cameras sold was 250,000 and is increasing at a rate of 12% per year. When will the number of digital cameras sold be equal to the number of film cameras sold?

Explanation / Answer

1) If the population quadruples every 15 hours, it must increase by a factor of 1.25 every 5 hours. (15/3=5, 4/3=1.25) assume in the beginning you have 10 bacteria. After 5 hours you have 10*1.25 bacteria. After 10 hours you have 10*1.25*1.25 (=10*1.25^2) bacteria After 15 hours you have 10*1.25*1.25*1.25 (=10*1.25^3) bacteria. After 20 hours you have 10*1.25^4 bacteria. After 30 hours you have 10*1.25^6 bacteria --> after 30 hours you have 1.25^2 times more bacteria than after 20 hours. 2) 100,000=100*2^t, where t= number of years --> 1000=2^t apply logarithms --> ln(1000)=ln(2^t)=t*ln(2) --> t=ln(1000)/ln(2)=9.966 years 3) Not enough information given. I have info about the number of rolls of film and digital cameras, but not any about the number of film cameras. There is no stated correlation between rolls of film and film cameras sold. Assuming that the first line was a typo and there were 3 million film cameras sold last year: At t, 3,000,000*(1-0.17)^t= number of film cameras sold At t, 250,000*(1+0.12)^t= number of digital cameras sold --> 250,000*1.12^t=3,000,000*0.83^t --> 1.12^t/0.83^t=(1.12/0.83)^t=1.3494^t=3,000,000/250,000=12 apply logarithms to both sides -->ln(1.3494^t)=t*ln(1.3494)=ln(12) -->t=ln(12)/ln(1.3494)=8.29242 years

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