Step-by-step explanation:
<u>Step 1: Determine the axis of symmetry</u>
The axis of symmetry is middle of the parabola. In this equation we see that at x = -1 we have the vertex and also the middle of the parabola. So our axis of symmetry is x = -1.
<u>Step 2: Determine the vertex</u>
The vertex is the minimum or maximum of a parabola and is bent in a crest form. In this example the vertex is at (-1, -3) because we are using the tip of the graph.
<u>Step 3: Determine the y-intercept</u>
The y-intercept is where the graph intersects with the y-axis. In this example we intersect the y-axis at -4 so that means that our point would be (0, -4) meaning that we intersect x = 0 at -4.
<u>Step 4: Determine if the vertex is a min or max</u>
Looking at the graph we can see that the rest of the red line is beneath the vertex point which means that the vertex is a max.
<u>Step 5: Determine the domain</u>
The domain is the x-values that we are going to be using and we know that we are reaching toward positive and negative inifity which means that we are using all real numbers.
<u>Step 6: Determine the range</u>
The range is the y axis and what y values we are able to reach using the graph. In this example we can see that all y-values above -3 are not being used therefore the range is 
Answer:
b b
Step-by-step explanation:v gv g
Answer:
Step-by-step explanation:
an exponential equation has the form y=ar^x where y=final amount, a=initial amount, r=rate, and x=time, in this case
y=200(1.18)^x
Answer:
Part a. t = 7.29 years.
Part b. t = 27.73 years.
Part c. p = $3894.00
Step-by-step explanation:
The formula for continuous compounding is: A = p*e^(rt); where A is the amount after compounding, p is the principle, e is the mathematical constant (2.718281), r is the rate of interest, and t is the time in years.
Part a. It is given that p = $2000, r = 2.5%, and A = $2400. In this part, t is unknown. Therefore: 2400 = 2000*e^(2.5t). This implies 1.2 = e^(0.025t). Taking natural logarithm on both sides yields ln(1.2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(1.2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(1.2)/0.025. This means that t = 7.29 years (rounded to the nearest 2 decimal places)!!!
Part b. It is given that p = $2000, r = 2.5%, and A = $4000. In this part, t is unknown. Therefore: 4000 = 2000*e^(2.5t). This implies 2 = e^(0.025t). Taking natural logarithm on both sides yields ln(2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(2)/0.025. This means that t = 27.73 years (rounded to the nearest 2 decimal places)!!!
Part c. It is given that A = $5000, r = 2.5%, and t = 10 years. In this part, p is unknown. Therefore 5000 = p*e^(0.025*10). This implies 5000 = p*e^(0.25). Making p the subject gives p = 5000/e^0.25. This means that p = $3894.00(rounded to the nearest 2 decimal places)!!!
Answer:
Correct
Step-by-step explanation: