Question

The population of a large city can be calculated using the function .P = 227,000(.98)^t What can you say about the rate of change from year 1 to year 2 compared to the rate of change from year 9 to year 10?

Answer 1

Answer:

872132.184

Step-by-step explanation:

hey using compound interest formula u can directly get the answer

Answer 2

Population of the city is decreasing at a slightly faster rate between year 9 and year 10 compared to the rate of decrease between year 1 and year 2.

The given function to calculate the population of a large city is:

$P = 227,000(.98)^t$

where t is the number of years.

To compare the rate of change from year 1 to year 2 with the rate of change from year 9 to year 10, we need to find the population for each of these years and calculate their respective rates of change.

Population after 1 year:

$P(1) = 227,000(.98)^1 = 222,460$

Population after 2 years:

$P(2) = 227,000(.98)^2 = 218,029.2$

Rate of change from year 1 to year 2:

$((P(2) - P(1))/P(1)) * 100%$

$= ((218,029.2 - 222,460)/222,460) * 100%$

= -1.99%

Population after 9 years:

$P(9) = 227,000(.98)^9 = 173,190.02$

Population after 10 years:

P$(10) = 227,000(.98)^10 = 169,627.202$

Rate of change from year 9 to year 10:

$((P(10) - P(9))/P(9)) * 100%$

=$((P(10) - P(9))/P(9)) * 100%$

= -2.05%

Therefore, we can see that the rate of change from year 9 to year 10 (-2.05%) is slightly higher than the rate of change from year 1 to year 2 (-1.99%).

This means that the population of the city is decreasing at a slightly faster rate between year 9 and year 10 compared to the rate of decrease between year 1 and year 2.

For similar question on Population rate of city

https://brainly.in/question/54442220

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