Write an exponential function to model the situation.A population of 300 animals decreased at an annual rate of 22%
1 answer:
Answer:
Step-by-step explanation:
x is the number of years. y is the population after x years.
Each year, the population decreases by 22%, since 100% - 22% = 78%, and 78% = 0.78, each year, the population is 0.78 of the previous year's population.
year zero: y = 300
year 1: y = 300 * 0.78 = 300 * (0.78)^1
year 2: y = (300 * 0.78) * 0.78 = 300 * (0.78)^2
year 3: y = ((300 * 0.78) * 0.78) * 0.78 = 300 * (0.78)^3
year x: y = 300(0.78)^x
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Given:
Principal amount = $2000
Rate of interest = 3.5% compounded quarterly.
Time = 6 years
To find:
The amount after 6 years.
Solution:
The formula for amount after compound interest is:
Where, P is principal, r is rate of interest in decimal, n is the number of time interest compounded in an year and t is the number of years.
The interest is compounded quarterly, so .
Substituting , we get
Approximate the value to the nearest hundredth.
The amount after 6 years us $2465.10. Therefore, the correct option is A.