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)!!!
Well that would be 8 apples in 4 bags so there’s 6
answer: 6
Answer:
y = 2.1x +5, 21 miles
Step-by-step explanation:
We will denote miles as "x"
Since she tipped the driver $5, that is a flat rate and that will be our y-intercept. Since it costs $2.10 per mile, we need to multiply that number by the number of miles
So our equation will be y = 2.1x +5
In order to figure out how many miles Ann lives from the airport, we need to substitute y for her grand total that she was charged
This gives us 49.10 = 2.10x + 5
First we need to subtract 5 from each side to get 44.10 = 2.10x
We then need to divide both sides by 2.10 to get 21 = x
Ann drove 21 miles
Then its midpoint = (-2, 3)
The formula to find the arc length L is
L = r*theta
where r is the radius and theta is the central angle in radians (this formula will not work if theta is in degrees)
If the central angle is 1 radian, then theta = 1 and
L = r*theta
L = r*1
L = r
So the arc length is the same as the radius
Answer: Choice A) The radius of the circle
