We are told that a population of insects grows exponentially and we are given a table of data about insect population growth. We are asked to find population of insects at the end of week 11.
The initial insect population is 20 and at the end of 1st week population increases to 30.
Let us find growth percentage of insect population,
![\text{Growth percentage}=\frac{\text{Difference}}{Actual} \cdot100](https://tex.z-dn.net/?f=%5Ctext%7BGrowth%20percentage%7D%3D%5Cfrac%7B%5Ctext%7BDifference%7D%7D%7BActual%7D%20%5Ccdot100)
![\text{Growth percentage}=\frac{\text{30-20}}{20} \cdot100](https://tex.z-dn.net/?f=%5Ctext%7BGrowth%20percentage%7D%3D%5Cfrac%7B%5Ctext%7B30-20%7D%7D%7B20%7D%20%5Ccdot100)
![\text{Growth percentage}=\frac{\text{10}}{20} \cdot100](https://tex.z-dn.net/?f=%5Ctext%7BGrowth%20percentage%7D%3D%5Cfrac%7B%5Ctext%7B10%7D%7D%7B20%7D%20%5Ccdot100)
![\text{Growth percentage}=0.5 \cdot100=50](https://tex.z-dn.net/?f=%5Ctext%7BGrowth%20percentage%7D%3D0.5%20%5Ccdot100%3D50)
We can see that insect population is growing at rate of 50% per week.
Now let us write an exponential function for our population.
, where P(w) represents population at the end of w weeks.
Let us substitute w=11 in our function to find insect population at the end of 11 weeks.
![P(11)=20(1+0.50)^{11}](https://tex.z-dn.net/?f=P%2811%29%3D20%281%2B0.50%29%5E%7B11%7D)
![P(11)=20(1.50)^{11}](https://tex.z-dn.net/?f=P%2811%29%3D20%281.50%29%5E%7B11%7D)
![P(11)=20\cdot 86.49755859375](https://tex.z-dn.net/?f=P%2811%29%3D20%5Ccdot%2086.49755859375)
![P(11)=1729.951171875\approx 1730](https://tex.z-dn.net/?f=P%2811%29%3D1729.951171875%5Capprox%201730)
Therefore, population of insects at the end of 11th week will be 1730.
Answer:
1 : 3
Step-by-step explanation:
1st Half: 9
2nd Half: 2(9)
Ratio = 2nd : 1st+2nd
9 : 9+2(9)
9 : 9 + 18
9 : 27
1 : 3
Answer:
You will get 210 pounds
Step-by-step explanation:
Step 1: Determine the exchange rate
Exchange rate=Value of US dollars/value of British pounds
where;
Value of US dollars=800
Value of British pound=560 pounds
replacing;
Exchange rate=800/560=1.43
This can be translated as;
1 British pound=1.43 US dollars
Step 2: Determine the value in pounds of 300 dollars
Value of British pounds=Value of US dollars/Exchange rate
where;
Value of US dollars=300
Exchange rate=1.43
replacing;
Value of British pounds=300/1.43
Value of British pounds=210
You will get 210 pounds
Answer:
2 students can get lemonade
Step-by-step explanation:
only 2 people can get the lemonade