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Days, Months, Years
Who Am I
You Write
Situational
100
Is the following growth or decay: y = 2^x
What is growth
100
The population in the town of Huntersville is presently 38,300. The town grows at an annual rate of 1.2%. Find the number of years it takes for the population to grow to 42,500. Round to the nearest whole year.
What is approximately 9 years
100
Use y = 250(1 + 0.2)^x
What is the initial amount?
What is 250
100
Write an exponential growth equation to model the situation. A population of 422,000 increases by 12% each year.
What is y= 422,000(1+.12)^t or
y=422,000(1.12)^t
100
A bacteria culture doubles every 0.25 hours. At time 1.25 hours, there are 40 000 bacteria present. How many bacteria were present initially?
What is 1250
Can you work backwards with a table:
200
Is the following growth or decay: y=100*(1/2)^x
What is decay
200
$1,200 is invested at an annual rate of 3.2%. Find the number of years it will take for the account balance to be $1,480. Round your answer to the nearest tenth.
What is approximately 6.7 years
200
Use y = 250(1.2)^x
What is the growth factor?
What is 1.2
200
The population of Baconburg starts off at 20,000, and grows by 13% each year. Write an exponential growth equation AND find the population after 10 years.
What is y = 20,000(1+.13)^x and population of 67,891 after 10 years
200
A bacteria culture triples every 4 hours and starts with 10 000 bacteria. Find the number of bacteria in the culture after 30 hours.
What is 37,879,951 or in Scientific Notation:
3.79E7
Equation:
y=10,000(3)^(x/4) time divided by 4 since it triples every 4 hours
300
Is the following growth or decay:
y= -100*(4)^x
What is growth
300
The population in the town of Deersburgh is presently 42,500. The town has been growing at a steady rate of 2.7%. Find the number of years ago that the population was 30,000.
What is approximately 13 years ago
300
Use y = 250(1 + 0.2)^t What is the growth
rate (%)?
What is 20%
300
The Hippityhoppity bunny decided to have a family reunion at the Magic Forest every 5 years beginning in 2019. During the second reunion in 2020, the family discovered that the number of family members was 154 and was growing at an annual rate of 3.2%. Write an equation to model the growth of the bunny family and calculate how many people attended the first reunion in 2019.
What is y = 154(1+.032)^x when x>=1
In 2019 the population would have been 149 (plug in -1 for x
300
The world population doubles every 35 years. In 1980 the population was 4.5 billion. Assuming that the doubling period remains at 35 years, estimate the population in the year 2120.
What is 72,000,000,000
The work: 2120-1980 is 140 years
140/35 is 4 times so the population doubles 4 times.
4.5*2=9 billion in the year (1980+35=2015)
9*2=18 billion in the year (2015+35=2050)
18*2=36 billion in the year (2050+35=2085)
36*2=72 billion in the year (2085+35=2120)
To write an equation:
y=4.5(2)^(x/35) in billions
400
What percent of growth/decay is represented by the function: y = 7 (0.06)^x
What is 94% decay
400
The value of a stock when purchased was $10 a share. The stock grew at a monthly rate of 7%. Find the number of months it took to reach a value of $15.75 a share. Round to the nearest tenth of a month.
What is approximately 6.7 months
400
y = 9.8(1.0035)^t What is the growth factor?
What is 1.0035
400
The fish in The Magic Forest Lake were declining at an annual rate at 1.5%. Their current number is estimated at 2500. Write an equation to model the decreasing number of fish.
What is y = 2500(1 - .015)^x or simplified:
y=2500(0.985)^x
400
A sodium isotope, Na^24 , has a half-life of 15 hours. Determine the amount of sodium that remains from a 4 g sample after 45 hours?
What is 0.5g
so in 15 hours 1/2 of the radioactive material remains
time grams
0 4
15 2
30 1
45 1/2
500
What is the rate of growth or decay:
y = -350 (7/4)^x
What is 75% growth
500
The value of a stock when purchased is $10 a share. The stock decreased at a rate of 3% daily. Find the number of days it took for the stock to be worth $7.40. Round your answer to the nearest whole day.
What is almost 10 days (approximately 9.9 days)
500
y = 4.2(1.085)^t What is the growth rate %?
What is 8.5%
500
The fish in The Magic Forest Lake were declining at an annual rate at 0.7%. Their current number is estimated at 15,000. Write an equation to predict the number of fish in the lake in 10 years.
What is y = 15,000(1-0.007)^x or
y=15000(0.993)^x
in ten years the population will be 13,982
500
A colony of insects doubles every 10 days. If the colony has 850 insects today, how many were present 10 days ago?
What is 425 insects
y=850(2)^(x/10)
when x=-10, 425 insects
Check
-10 425
0 850
425*2=850