Absolute increase = 4150 - 3300 = 850
Relative increase = (absolute increase/original population) x 100
= (850/3300) x 100
= 25.76%
Therefore, the absolute increase in the population of the town is 850 and the relative increase is 25.76%.
population of a town increased from 3300 to 4150 find absolute and relative increase
5 answers
Starting in the year of 2012 the number of speeding tickets issued each year during 2012 issued 170 every year thereafter the number of tickets issued predicted to grow by 5%
If Pn denotes the predicted number of tickets during 2012 +n then write recursive formula for Pn
If Pn denotes the predicted number of tickets during 2012 +n then write recursive formula for Pn
The recursive formula for Pn can be written as:
Pn = Pn-1 + 0.05Pn-1
where Pn-1 represents the predicted number of tickets issued in the previous year (2012 + n - 1).
The formula states that to predict the number of tickets issued in the current year (2012 + n), we take the predicted number of tickets in the previous year and add 5% of that value to it. This recursion continues until the desired year is reached.
Pn = Pn-1 + 0.05Pn-1
where Pn-1 represents the predicted number of tickets issued in the previous year (2012 + n - 1).
The formula states that to predict the number of tickets issued in the current year (2012 + n), we take the predicted number of tickets in the previous year and add 5% of that value to it. This recursion continues until the desired year is reached.
Starting in the year of 2012 the number of speeding tickets issued each year during 2012 issued 170 every year thereafter the number of tickets issued predicted to grow by 5%
If Pn denotes the predicted number of tickets during 2012 +n then write recursive formula for Pn
How many tickets predicted to be issued 2028
If Pn denotes the predicted number of tickets during 2012 +n then write recursive formula for Pn
How many tickets predicted to be issued 2028
Using the recursive formula we can find the predicted number of speeding tickets issued in 2028:
Pn = Pn-1 + 0.05Pn-1
where n = 16 (since we want the number of tickets in 2028, which is 16 years after 2012)
We know that P0 = 170 (since 170 tickets were issued in 2012).
So, we can compute P16 as follows:
P16 = P15 + 0.05P15
P15 = P14 + 0.05P14
P14 = P13 + 0.05P13
and so on, until we get to P0.
P16 = P15 + 0.05P15
= (P14 + 0.05P14) + 0.05(P14 + 0.05P14)
= (P13 + 0.05P13) + 0.05(P13 + 0.05P13) + 0.05(P13 + 0.05P13) (expanding P14)
= (P12 + 0.05P12) + 0.05(P12 + 0.05P12) + 0.05(P12 + 0.05P12) + 0.05(P12 + 0.05P12) (expanding P13)
and so on, until we get to P0.
Carrying out this calculation, we get:
P16 = 170 * (1 + 0.05)^16
= 170 * 2.113
= 359.11 (rounded to two decimal places)
Therefore, the predicted number of speeding tickets issued in 2028 is 359.11.
Pn = Pn-1 + 0.05Pn-1
where n = 16 (since we want the number of tickets in 2028, which is 16 years after 2012)
We know that P0 = 170 (since 170 tickets were issued in 2012).
So, we can compute P16 as follows:
P16 = P15 + 0.05P15
P15 = P14 + 0.05P14
P14 = P13 + 0.05P13
and so on, until we get to P0.
P16 = P15 + 0.05P15
= (P14 + 0.05P14) + 0.05(P14 + 0.05P14)
= (P13 + 0.05P13) + 0.05(P13 + 0.05P13) + 0.05(P13 + 0.05P13) (expanding P14)
= (P12 + 0.05P12) + 0.05(P12 + 0.05P12) + 0.05(P12 + 0.05P12) + 0.05(P12 + 0.05P12) (expanding P13)
and so on, until we get to P0.
Carrying out this calculation, we get:
P16 = 170 * (1 + 0.05)^16
= 170 * 2.113
= 359.11 (rounded to two decimal places)
Therefore, the predicted number of speeding tickets issued in 2028 is 359.11.