Note: Use the information below to answer each part of the question, and show all necessary work. You can type or upload your work in the space provided. An adult takes 600 mg of ibuprofen. Each hour, the amount of ibuprofen in the person's system decreases by about 29%. a) Write an exponential function to model this situation. (2 pts) b) About how much ibuprofen would be in the person's system after 5 hours? (2 pts) c) After about how many hours would there be 30 mg of ibuprofen left in their system? (3 pts) (7 points)
a) To model this situation, we can use the formula for exponential decay:
A(t) = A₀ * (1 - r)^t
where A(t) is the amount of ibuprofen in the person's system at time t (in hours), A₀ is the initial amount of ibuprofen (600 mg), r is the decay rate (0.29), and t is the time in hours.
So, the exponential function to model this situation would be:
A(t) = 600 * (1 - 0.29)^t
b) To find the amount of ibuprofen in the person's system after 5 hours, we substitute t = 5 into the exponential function:
A(5) = 600 * (1 - 0.29)^5
≈ 600 * 0.51^5
≈ 600 * 0.87808
≈ 526.85 mg
Therefore, about 526.85 mg of ibuprofen would be in the person's system after 5 hours.
c) To find the number of hours it takes for there to be 30 mg of ibuprofen left in the person's system, we set A(t) = 30 and solve for t:
30 = 600 * (1 - 0.29)^t
Divide both sides by 600:
0.05 = (1 - 0.29)^t
Take the logarithm of both sides:
log(0.05) = log((1 - 0.29)^t)
Using logarithm properties, we can bring down the t as an exponent:
log(0.05) = t * log(1 - 0.29)
Divide both sides by log(1 - 0.29):
t = log(0.05) / log(1 - 0.29)
≈ 7.1278
Therefore, after about 7.1278 hours, there would be 30 mg of ibuprofen left in the person's system.
Match each variable below with the correct description of how it transforms the graph of an exponential function. y=a(b)x−h+k (2 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. k h
k: vertical shift
h: horizontal shift
Which graph best represents y=−2x+1 ?(1 point) Responses Skip to navigation
I'm sorry, but I am unable to provide visual representations or graphs. However, I can explain how to interpret the equation y = -2x + 1.
The equation y = -2x + 1 represents a linear function. The coefficient -2 in front of x indicates the slope of the line, which is the amount by which y changes for every 1 unit increase in x. In this case, since the coefficient is negative, the line will have a negative slope, meaning it will slope downwards from left to right.
The constant term 1 at the end of the equation represents the y-intercept, which is the point where the line intersects the y-axis. In this case, the line intersects the y-axis at y = 1.
Based on this information, you can sketch a graph of the line by plotting the y-intercept (0, 1) and using the slope to find additional points on the line.
Question Some investments in the stock market have earned 10 % annually. At this rate, earnings can be found using the formula A=P(1.10)n , where A is the total value of the investment, P is the initial value of the investment, and n is the number of years the money is invested. If $15,00 is invested in the stock market at this annual rate of return, what is the expected total value after 19 years?(1 point) Responses $9,173.86 $9,173.86 $28,050.00 $28,050.00 $8,339.88 $8,339.88 $7,581.71 $7,581.71 Skip to navigation
To find the expected total value after 19 years, we can use the formula A = P(1.10)^n, where P is the initial value of the investment and n is the number of years.
In this case, P is $15,000 and n is 19.
A = 15,000(1.10)^19
Using a calculator, we can calculate:
A ≈ $28,049.99
Therefore, the expected total value after 19 years is approximately $28,050.00.
What is the value of log162 ?(1 point) Responses 12 1 half 14 1 fourth 18 1 eighth 8
To find the value of log162, you can use the logarithm property:
log_b(x) = y if and only if b^y = x
In this case, we want to find the exponent y such that 2^y = 162.
If we break down 162 into its prime factors, we have:
162 = 2^1 * 3^4
So, we can rewrite the equation as:
2^y * 3^0 = 2^1 * 3^4
Comparing the exponents, we have:
y = 1
Therefore, the value of log162 is 1.