23. Suppose the number of expert gamers in California is 52,400 and is growing 20% each year. Predict the number of experts after 5 years.

24. The population of bacteria in your messy room is 36,725 and is growing at a rate of 11% each month. What would the population be after 6 months if you don’t clean your room?


25. The current popularity of the Kardashians is about 82,302 fans.gladly, this is falling at a rate of 50% each year. How many fans will the Kardashians have in 4 years?

26. The number of active Snapchat users is about 23,000,000 people. This number is falling at a rate of 5% each month. How many Snapchat users will there be in one year?

27. You put $5,000 in an account that is compounded quarterly. The annual interest rate, r, is 4%. How much will be in the account after 10 years?

28. You just got a job and you want to start saving for a car. You put $1500 in a savings account that is compounded monthly. The annual interest rate is 8.5% How much money will you have saved in 3 years?

If someone could simply Explain these to me-it would mean alot

23. 52,400 + 52,400*0.2*5 =

24. 36,725 + 36,725*0.11*6 =
25. 82,302 - 82302*05*4 =. I believe it should be 5% instead of 58%. Check textbook.
26. Same procedure #25, but change 1yr. to 12 mo.
27. P = Po(1+r)^n,
Po = $5,000,
r = 0.04/4 = 0.01 = quarterly % rate.
n = 4 Comp./yr. * 10 yrs. = 40 Compounding periods.

28. P = Po(1+r)^n,

Po = $1500,
r = 0.085/12 = 0.0071 = Monthly % rate.
n = 1comp./mo. * 36mo. = 36 Compounding periods.

23. To predict the number of expert gamers in California after 5 years, we can use the formula for compound growth:

A = P(1 + r)^n

Where:
A = final amount
P = initial amount
r = growth rate
n = number of years

In this case, we have:
P = 52,400 (initial number of expert gamers)
r = 20% (growth rate, expressed as a decimal)
n = 5 (number of years)

Using these values, we can calculate the final amount:

A = 52,400(1 + 0.20)^5 = 124,827.2

Therefore, the predicted number of expert gamers in California after 5 years would be approximately 124,827.

24. To determine the population of bacteria in your messy room after 6 months, we can again use the formula for compound growth:

A = P(1 + r)^n

Where:
A = final population
P = initial population
r = growth rate
n = number of months

In this case, we have:
P = 36,725 (initial population of bacteria)
r = 11% (growth rate, expressed as a decimal)
n = 6 (number of months)

Using these values, we can calculate the final population:

A = 36,725(1 + 0.11)^6 = 63,418.45

Therefore, if you don't clean your room, the estimated population of bacteria after 6 months would be approximately 63,418.

25. To calculate the number of fans the Kardashians will have in 4 years, we can use the formula for compound decay:

A = P(1 - r)^n

Where:
A = final number of fans
P = initial number of fans
r = decay rate
n = number of years

In this case, we have:
P = 82,302 (initial number of fans)
r = 50% (decay rate, expressed as a decimal)
n = 4 (number of years)

Using these values, we can calculate the final number of fans:

A = 82,302(1 - 0.50)^4 = 20,575.5

Therefore, the Kardashians are predicted to have approximately 20,576 fans in 4 years.

26. To determine the number of Snapchat users in one year, we can again use the formula for compound decay:

A = P(1 - r)^n

Where:
A = final number of users
P = initial number of users
r = decay rate
n = number of months

In this case, we have:
P = 23,000,000 (initial number of Snapchat users)
r = 5% (decay rate, expressed as a decimal)
n = 12 (number of months in a year)

Using these values, we can calculate the final number of users:

A = 23,000,000(1 - 0.05)^12 = 14,376,740.79

Therefore, there are predicted to be approximately 14,376,741 Snapchat users after one year.

27. To calculate the amount in the account after 10 years, we can use the formula for compound interest:

A = P(1 + r/n)^(n*t)

Where:
A = final amount
P = initial amount
r = annual interest rate, expressed as a decimal
n = number of times interest is compounded per year
t = number of years

In this case, we have:
P = $5,000 (initial amount)
r = 4% (annual interest rate, expressed as a decimal)
n = 4 (compounded quarterly)
t = 10 (number of years)

Using these values, we can calculate the final amount:

A = 5000(1 + 0.04/4)^(4*10) = $7,295.96

Therefore, there will be approximately $7,295.96 in the account after 10 years.

28. To determine how much money you will have saved in 3 years, we can again use the formula for compound interest:

A = P(1 + r/n)^(n*t)

Where:
A = final amount
P = initial amount
r = annual interest rate expressed as a decimal
n = number of times interest is compounded per year
t = number of years

In this case, we have:
P = $1,500 (initial amount)
r = 8.5% (annual interest rate, expressed as a decimal)
n = 12 (compounded monthly)
t = 3 (number of years)

Using these values, we can calculate the final amount:

A = 1500(1 + 0.085/12)^(12*3) = $1,734.94

Therefore, you will have approximately $1,734.94 saved in 3 years.

23.

52,400 * 0.2 * 5

24. Same as 23. Multiply the number of bacteria by the rate by the time.

If you post your answers and work for these problems, we'll be glad to check them.