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The function h(x)=2x+5 models the cost (in dollars) of renting a scooter for x hours.
Write down the cost of renting the scooter for 3 hours.
Solve h(x)=15.
State the gradient of the function and explain what it represents in this context.
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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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At the end of the 2024 fishing season on Fork Lake, 60 anglers (amateur fishers) were randomly surveyed. They were asked how many bass they caught over the whole season. The information is summarized in the following frequency table:
Assume that this sample is representative of all anglers in any season, and that all anglers have equal skill.
State the value of k.
For the 2025 season estimate
the probability a randomly selected angler will catch fish,
the expected number of fish caught by an angler over the season.
The U.S Fish and Wildlife Service (USFWS) estimates that the bass population in Lake Fork will grow by 8% between the 2024 and 2025 fishing seasons.
Given that the bass population was 110′000 at the end of the 2024 season, estimate the number of bass in the Lake at the opening of the 2025 season.
The USFWS wants the bass population to remain unchanged year to year.
How many seasonal fishing permits should be granted in 2025? Give your answer to the nearest hundred.
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The blades of a wind turbine have a diameter of 16m and rotate clockwise at a constant speed, 1 revolution every 4 seconds. The blades are fixed on a shaft such that the tips of the blades are always at least 7m above the ground. The point Q lies at the tip of one of the blades.
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Let h be the height, in meters, of Q above the ground. After t minutes, h is given by h(t)=acos(bt)+c, where a,b,c∈R and a>0.
Show that Q starts at the highest possible point.
Find the values of a, b and c.
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