Are my answers correct?
a. The number of bacteria present in a colony is 180 at 12 noon. The bacteria grows at a rate of 23% per hour.
How many will be present at 8pm?
Answer: ~943 number of Bacteria by 8pm
b. A house purchased for $226,000 has lost 3% of its value each year for the past 5 years. What is the house worth now?
answer: FV = $194,073.89
what the house will be worth in 5 years.
a. time elapsed= 8 hours
number= 180(1.23)^8=
b. worth= 226,000(1-.03)^5=
a. Growth factor = 100% + 23% = 123% = 1.23.
Bacteria = 180 *1.23^8 = 943.
b. Value = 226,000 - 0.03*226,000*5 = $192,100.
Correction: disregard my response to part b; I agree with bob' s answer.
a. To find the number of bacteria present at 8pm, we need to calculate the growth rate starting from 12 noon to 8pm.
Given:
Number of bacteria at 12 noon = 180
Growth rate per hour = 23%
To calculate the number of bacteria at 8pm, we can use the compound interest formula:
Final Value = Initial Value * (1 + Growth Rate)^Time
In this case, the initial value is 180 bacteria, the growth rate is 23% (or 0.23), and the time is 8 hours.
Number of bacteria at 8pm = 180 * (1 + 0.23)^8
= 180 * (1.23)^8
≈ 943
Therefore, the number of bacteria at 8pm is approximately 943.
b. To find the current value of the house after losing 3% of its value each year for the past 5 years, we need to calculate the future value using the compound interest formula.
Given:
Initial value of the house = $226,000
Loss rate per year = 3%
To calculate the future value, we can use the compound interest formula as well:
Final Value = Initial Value * (1 - Loss Rate)^Time
In this case, the initial value is $226,000, the loss rate is 3% (or 0.03), and the time is 5 years.
House worth now = $226,000 * (1 - 0.03)^5
= $226,000 * (0.97)^5
≈ $194,073.89
Therefore, the current worth of the house is approximately $194,073.89.