The population of a city is modeled by the equation P(t) = 256,114e0.25t where t is measured in years. If the city continues to grow at this rate, how many years will it take for the population to reach one million?
Answers
Answer: it take 5.448 years for the population to reach one million.
Step-by-step explanation:
The population of a city is modeled by the equation
P(t) = 256,114e0.25t
where t is measured in years.
For the population to reach 1000000, it means that
1000000 = 256114e0.25t
1000000/256114 = e0.25t
3.9045 = e0.25t
Taking ln of both sides of the equation, it becomes
Ln 3.9045 = Ln e0.25t
1.362 = 0.25t
t = 1.362/0.25
t = 5.448 years
Final answer:
The city's population is modeled by an exponential function and to find when the population will reach one million, we need to solve the equation for t by setting P(t) = 1,000,000. This requires dividing by the initial population, taking the natural logarithm, and then dividing by the growth rate (0.25). The result is the time in years it takes for the city's population to reach one million.
Explanation:
Calculation of Population Growth Time
The city's population growth is modeled by an exponential function, P(t) = 256,114e0.25t. Here, P(t) is the population at time t and 'e' is Euler's number, approximately equal to 2.71828. Your goal is to find when the population reaches one million.
To do this, set P(t) = 1,000,000 and solve for t:
1,000,000 = 256,114e0.25t
You would divide both sides by 256,114 and then take the natural logarithm to isolate t:
t = ln(1,000,000 / 256,114) / 0.25
Use a calculator to solve for 't'. This gives the time in years it takes for the city's population to reach one million people. It's a clear demonstration of how exponential growth operates: as the population increases, it takes less time to add a certain number of individuals.
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Paul, Colin and Brian are waiters. One night the restaurant earns tips totalling £77.40. They share the tips in the ratio 1:3:5. How much more does Brian get over Paul?
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Answer:
Step-by-step explanation:
the answer is 14
Answers
Your answer should be a polynomial in standard form.
3x^2
+
8x
+
7
7x^2
Area =
What is the area
Answers
Final answer:
The area of the rectangle is found by multiplying the length and the width together, giving the polynomial 21x^4 + 56x^3 + 49x^2.
Explanation:
The area of a rectangle can be found by multiplying the length by the height. In this case, the height of the rectangle is 7x^2 and the width of the rectangle is 3x^2 + 8x + 7
So, we multiply these two expressions together to get the area:
Area = 7x^2 * (3x^2 + 8x + 7) = 21x^4 + 56x^3 + 49x^2.
This is a polynomial and it is in standard form, as the terms are ordered from highest degree to lowest degree.
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Answer:
Step-by-step explanation:
Answers
using the expression 14.99(n) + 4.99, the total of 3 CDs would cost $49.96.
Answers
Answers
Answer:
C
Step-by-step explanation:
Let's say the cost of one sandwich is "s" and the cost of one drink is "d". From the first customer's order, we know that 3 sandwiches and 2 drinks cost $14.70. So we can write the equation: 3s + 2d = 14.70 From the second customer's order, we know that 2 sandwiches and 4 drinks cost $13.30. So we can write the equation: 2s + 4d = 13.30 Now, we can solve this system of equations to find the values of "s" and "d". Multiplying the first equation by 2 and the second equation by 3, we get: 6s + 4d = 29.40 6s + 12d = 39.90 Subtracting the first equation from the second equation, we get: 6s + 12d - (6s + 4d) = 39.90 - 29.40 Simplifying, we have: 8d = 10.50 Dividing both sides by 8, we find: d = 1.3125 Now we can substitute this value back into either of the original equations to find the value of "s". Let's use the first equation: 3s + 2(1.3125) = 14.70 Simplifying, we have: 3s + 2.625 = 14.70 Subtracting 2.625 from both sides, we find: 3s = 12.075 Dividing both sides by 3, we get: s = 4.025 So the cost of one sandwich is approximately $4.03 and the cost of one drink is approximately $1.31. Therefore, the correct answer is: c) Sandwich: $4.03, Drink: $1.31
Final answer:
Option (a), with the cost of a sandwich as $3.50 and a drink as $2.35, is the correct solution for this algebraic problem. This conclusion was reached by forming two equations from the information given and solving this system of equations.
Explanation:
This is an algebra problem where we set up two equations to solve for two variables. Let's denote the cost of a sandwich as S and the cost of a drink as D. The first equation derived from the first customer's purchase would be 3S + 2D = 14.70. The second equation from the second customer's purchase would be 2S + 4D = 13.30. To solve these equations, we could multiply the first equation by 2 and the second equation by 3 then subtract the second equation from the first. This will provide the cost of a Sandwich which can then be substituted back into either original equation to get the cost of a Drink. Once you solve this system, the answer appears as option (a): Sandwich $3.50 and Drink $2.35.
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