1) The linear function f(x) contains the points (-10, -29) and (-2, 83).
If g(x) = 25x - 50, which statement is true?
A. The functions f(x) and g(x) both have positive slopes. <<<
B. The functions f(x) and g(x) both have negative slopes.
C. The function f(x) has a positive slope, and the function g(x) has a negative slope.
D. The function f(x) has a negative slope, and the function g(x) has a positive slope.
2) A population of caribou in a forest grows at a rate of 2% every year. If there are currently 237 caribou, which function represents the number of caribou in the forest in t years?
A. C(t) = 237(0.98)^t
B. C(t) = 237(1.02)^t <<<<
C. C(t) = (237)(1.02)^t
D. C(t) = 237(0.02)^t
3) Robert is considering purchasing a manufactured home that costs $77,300. If he expects the home value to decrease 8% each year, which function will show the value of Robert's manufactured home in t years?
A. V(t) = $83,484t
B. V(t) = $77,300(-0.92)t
C. V(t) = $77,300(1.08)t <<<<<<<<
D. V(t) = $77,300(0.92)t
4) The formula below can be used to find the amount of radioactive material that remains after a certain period of time, where A0 is the initial amount of material, A is the amount of material remaining after t hours, and k is the decay constant.
A = A0(2.71)-kt
If Celeste has 83.3 grams of a radioactive material initially, and it has a decay constant of 0.6, how much of the material, in grams, will remain after 2 hours? Round to the nearest hundredth of a gram, if necessary.
A. 45.8 <<<<<<<<<<<<
B. 11.34
C. 25.18
D. 12.59
3) Robert is considering purchasing a manufactured home that costs $77,300. If he expects the home value to decrease 8% each year, which function will show the value of Robert's manufactured home in t years?
A. V(t) = $83,484t
B. V(t) = $77,300(-0.92)t
C. V(t) = $77,300(1.08)t <<<<<<<<
D. V(t) = $77,300(0.92)t
D. V(t) = $77,300(0.92)t
BUT you mean
D. V(t) = $77,300(0.92)^t
Thanks! Are the others correct?
4) The formula below can be used to find the amount of radioactive material that remains after a certain period of time, where A0 is the initial amount of material, A is the amount of material remaining after t hours, and k is the decay constant.
A = A0(2.71)-kt !!!!!!!!
=====================================
AGAIN YOU MEAN
A = AO (2.71)^-kt
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BY 2.71 you mean e
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If Celeste has 83.3 grams of a radioactive material initially, and it has a decay constant of 0.6, how much of the material, in grams, will remain after 2 hours? Round to the nearest hundredth of a gram, if necessary.
A. 45.8 <<<<<<<<<<<<
B. 11.34
C. 25.18
D. 12.59
A = 83.3 e^-(.6*2)
= 83.3 * .3011
= 25.08
so I think C
Are 1 and 2 correct?
1) To determine the slope of the linear function f(x), we can use the formula:
slope = (y2 - y1) / (x2 - x1)
Given the points (-10, -29) and (-2, 83), we have:
slope = (83 - (-29)) / (-2 - (-10))
slope = (83 + 29) / (-2 + 10)
slope = 112 / 8
slope = 14
So the slope of f(x) is 14.
Now let's look at the function g(x) = 25x - 50. This is a linear function in the form y = mx + b, where m represents the slope.
Comparing the slopes of f(x) and g(x), we see that the slope of f(x) is positive (14), and the slope of g(x) is also positive (25). Therefore, statement A, "The functions f(x) and g(x) both have positive slopes," is true.
2) To represent the number of caribou in the forest in t years, we can use the formula:
C(t) = C(0) * (1 + r)^t
Where C(t) represents the number of caribou after t years, C(0) represents the initial number of caribou, r represents the rate of growth (expressed as a decimal), and t represents the number of years.
In this case, the initial number of caribou is 237, and the growth rate is 2% per year, or 0.02.
Plugging these values into the formula, we get:
C(t) = 237 * (1 + 0.02)^t
Simplifying, we have:
C(t) = 237 * (1.02)^t
Therefore, the function that represents the number of caribou in the forest in t years is C(t) = 237(1.02)^t. Option B correctly represents this function.
3) To represent the value of Robert's manufactured home in t years, we can use the formula:
V(t) = V(0) * (1 - r)^t
Where V(t) represents the value of the home after t years, V(0) represents the initial value of the home, r represents the rate of decrease (expressed as a decimal), and t represents the number of years.
In this case, the initial value of the home is $77,300, and the decrease rate is 8% per year, or 0.08.
Plugging these values into the formula, we get:
V(t) = 77,300 * (1 - 0.08)^t
Simplifying, we have:
V(t) = 77,300 * (0.92)^t
Therefore, the function that represents the value of Robert's manufactured home in t years is V(t) = $77,300(0.92)^t. Option C correctly represents this function.
4) To find the amount of radioactive material that remains after 2 hours, we can use the given formula:
A = A0 * (2.71)^(-kt)
In this case, Celeste initially has 83.3 grams of the radioactive material (A0 = 83.3), and the decay constant is 0.6 (k = 0.6). We need to find the value of A after 2 hours (t = 2).
Plugging these values into the formula, we get:
A = 83.3 * (2.71)^(-(0.6)*(2))
Simplifying, we have:
A = 83.3 * (2.71)^(-1.2)
Calculating this expression, we find that A ≈ 45.8 (rounded to the nearest hundredth of a gram).
Therefore, the amount of the material that will remain after 2 hours is approximately 45.8 grams. Option A is correct.