Hey!! I would SUPER appreciate it if you could help me with these! Thank you! :)
1. Astronomers measure large distances in light-years. One light-year is the distance that light can travel in one year, or approximately 5.88 x 1012 miles. Suppose a star is 6.3 x 102 light-years from Earth. In scientific notation, approximately how many miles is it?
2. A dinosaur fossil is 128, 320,000 years old. How can you express this age in scientific notation with the highest level of precision?
3. Electromagnetic waves travel at a rate of 3 x 108 meters per second. How many seconds would it take for an electromagnetic wave to travel from a satellite to the surface of the Earth if the satellite is orbiting at a height of 2.9 x 109 meters? (Hint: Time is distance divided by rate)
4. Does the rule y=-5(7𝑥) represent an exponential function?
5. 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.
6. Suppose the number of bacteria growing in a culture dish doubles every 6 hours. If the culture dish initially contains 250 bacteria, how many bacteria are in the dish after 18 hours.
7. 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?
8. The current popularity of the Kardashians is about 82,302 fans. Sadly, this is falling at a rate of 50% each year. How many fans will the Kardashians have in 4 years?
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9. 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?
Equation:
Solution:
10. 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?
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11. 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?
Equation:
Solution:
6. 4,000
7. 609,63.5
8. 41,151
10. 460,000,000
11. 20,000
12. 38,250
Sure! I'd be happy to help you with these questions. Let's go step by step.
1. The star is 6.3 x 10^2 light-years from Earth. To find approximately how many miles it is, we can multiply this distance by the definition of 1 light-year in miles: 5.88 x 10^12 miles.
So, the calculation is: (6.3 x 10^2) * (5.88 x 10^12) = 3.70 x 10^15 miles.
Therefore, the star is approximately 3.70 x 10^15 miles away from Earth.
2. The dinosaur fossil is 128,320,000 years old. To express this age in scientific notation with the highest level of precision, we need to make sure there is only one digit before the decimal point.
So, we can rewrite the age as: 1.2832 x 10^8 years.
Therefore, the age of the dinosaur fossil in scientific notation with the highest level of precision is 1.2832 x 10^8 years.
3. Electromagnetic waves travel at a rate of 3 x 10^8 meters per second. To calculate how many seconds it would take for an electromagnetic wave to travel from the satellite to the surface of the Earth, given that the satellite is orbiting at a height of 2.9 x 10^9 meters, we can use the equation: Time = Distance / Rate.
So, the calculation is: (2.9 x 10^9 meters) / (3 x 10^8 meters per second) = 9.667 seconds.
Therefore, it would take approximately 9.667 seconds for the electromagnetic wave to travel from the satellite to the surface of the Earth.
4. The rule y = -5(7x) does not represent an exponential function. It represents a linear function, specifically a line with a negative slope.
5. The number of expert gamers in California is 52,400 and it is growing 20% each year. To predict the number of experts after 5 years, we can use the equation for exponential growth: A = P(1 + r)^t, where A is the final amount, P is the initial amount, r is the growth rate, and t is the time.
So, the calculation is: 52,400(1 + 0.2)^5 = 99,198.4.
Therefore, the predicted number of experts after 5 years is approximately 99,198.
I will continue with the remaining questions in the next response.
Of course, I'd be happy to help you with these questions! Here are the explanations and solutions for each question:
1. To find the approximate number of miles for a star that is 6.3 x 10^2 light-years away, you need to multiply the number of light-years by the number of miles in one light-year. In scientific notation, 5.88 x 10^12 represents the number of miles in one light-year. So, you can multiply 6.3 x 10^2 by 5.88 x 10^12 to get the approximate result.
2. To express the age of a dinosaur fossil, 128,320,000 years, in scientific notation with the highest level of precision, you can simply write it as 1.2832 x 10^8.
3. The time it takes for an electromagnetic wave to travel from a satellite to the surface of the Earth can be found using the formula "time = distance / rate". In this case, the distance is 2.9 x 10^9 meters and the rate is 3 x 10^8 meters per second. Dividing the distance by the rate will give you the time in seconds.
4. The rule y=-5(7𝑥) does not represent an exponential function. It is a linear equation since it describes a straight line with a fixed slope (-35) and no exponentiation involved.
5. To predict the number of expert gamers in California after 5 years, you can use the growth formula "final amount = initial amount * (1 + growth rate)^number of years". In this case, the initial amount is 52,400, the growth rate is 20% (or 0.20), and the number of years is 5. Plug these values into the formula to obtain the predicted number of experts after 5 years.
6. Since the number of bacteria doubles every 6 hours, you can use the formula "final amount = initial amount * 2^(number of doubling periods)" to find the number of bacteria after 18 hours. In this case, the initial amount is 250 and the number of doubling periods is 3 (since 18 hours / 6 hours = 3).
7. To determine the population of bacteria in your messy room after 6 months, you can use the growth formula "final population = initial population * (1 + growth rate)^number of months". In this case, the initial population is 36,725, the growth rate is 11% (or 0.11), and the number of months is 6. Plug these values into the formula to get the final population.
8. To calculate the number of fans the Kardashians will have in 4 years, you can use the formula "final amount = initial amount * (1 - decrease rate)^number of years". In this case, the initial amount is 82,302, the decrease rate is 50% (or 0.50), and the number of years is 4. Plug these values into the formula to obtain the final number of fans.
9. The number of Snapchat users in one year can be found using the formula "final amount = initial amount * (1 - decrease rate)^number of months". In this case, the initial amount is 23,000,000, the decrease rate is 5% (or 0.05), and the number of months is 12 (since there are 12 months in a year). Plug these values into the formula to get the final number of users.
10. To calculate the amount in the account after 10 years, compounded quarterly, you can use the compound interest formula "final amount = initial amount * (1 + interest rate/compounding periods)^(compounding periods * number of years)". In this case, the initial amount is $5,000, the interest rate is 4% (or 0.04), the compounding periods are 4 (since it is compounded quarterly), and the number of years is 10. Plug these values into the formula to obtain the final amount.
11. To determine the amount of money you will have saved in 3 years, compounded monthly, you can use the compound interest formula again. The initial amount is $1500, the interest rate is 8.5% (or 0.085), the compounding periods are 12 (since it is compounded monthly), and the number of years is 3. Plug these values into the formula to get the final amount.
By "help" do you mean do your homework assignment for you? What are your answers? If you truly have no ideas on any of them, you have some serious studying to do.
Just to start,
#11. 1500(1 + .085/4)^(4*3) = _____