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0 / 4
The function P(t)=200⋅1.05t models the population of a small town after t years.
Write down the initial population of the town.
Find the population after 2 years.
State, with justification whether the population is increasing or decreasing.
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0 / 5
A solar farm records its power output (in kilowatt-hours) once every hour from 10 a.m. to 2 p.m. The data are shown below, where t is hours after 10 a.m. and P(t) is the power generated in that hour.
Use the trapezoidal rule with an interval width of 1 to estimate the total energy generated between 10 a.m. and 2 p.m..
A high-precision meter later shows the true total was 325 kWh.
Calculate the percentage error of your estimate from part (a).
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0 / 5
A pollutant’s concentration in a river (in mg/L) at time t hours after a spill can be estimated by the following table:
Estimate the total pollutant exposure with a step size h=1 by using the trapezoidal rule.
It is known that the total exposure is actually 39Lmg⋅h.
Find the percent error of your estimate from part (a).
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0 / 6
The total market value of all the gold in the world is 2.7×1013 US dollars.
Given that a kilogram of gold costs $110000, calculate the mass of all the gold in the world.
Olympic swimming pools have dimensions 50m by 25m by 2m. It is given that 1cm3 of gold weighs 19g.
Find the number of olympic swimming pools needed to store all the world's gold.
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0 / 6
A spherical raindrop has a diameter of 2mm.
Find the volume of the raindrop in cm3.
In the following parts of the problem, give all your answers in the form a×10k where 1≤a<10 and k∈Z.
During a large thunderstorm, 7000m3 of water falls.
Estimate the number of raindrops that fell.
The number of HX2O molecules in 1mL is 3.34×1022.
Calculate the number of HX2O molecules that fell during the storm.
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0 / 5
The matrix below shows the selling price (in USD) of three snack packs S1,S2 and S3 at two vending machines A and B.
A student club places an order of 50 of S1, 80 of S2, and 40 of S3.
Write down a matrix equation for the total revenue vector R (2×1) from each machine.
Hence calculate the total revenue from vending‑machine A and from vending‑machine B.
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0 / 5
The regional sales of three products A, B and C by two branches, North and South, are given (in units) by the matrix
where the first row is North and the second is South. The shipping rate (in $USD per unit) charged by Carrier 1 and Carrier 2 for each product is
where rows correspond to products A, B, and C and columns to Carriers 1 and 2 respectively.
Write down a matrix equation for the total shipping‑cost matrix C, and hence find C.
For each branch, state which carrier is cheapest.
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0 / 8
The number of tilapia, catfish and trout harvested (in units) by Farm A and Farm B during a season is given by the matrix
where the first row is Farm A and the second is Farm B. Each fish species has an average weight (kg) and a selling price (USD) per fish, as shown by
where rows correspond to tilapia, catfish and trout, and columns correspond to weight and price respectively.
Find the total weight–revenue matrix T.
For each farm, determine
the total weight harvested (kg);
the total revenue earned (USD);
Hence state which farm has the higher revenue per kg.
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0 / 5
A system of equations is given by
Write this system in the form Ax=b, and find A−1.
Hence solve for (x,y,z).