A spherical balloon is being inflated. The radius of the balloon is increasing at the rate of 6 cm/s. (a) Find a function f that models the radius as a function of time t, in seconds. f(t) = (b) Find a function g that models the volume as a function of the radius r, in cm. g(r) = %3D (c) Find g o f. gof = What does this function represent? O The function represents the volume as a function of time. The function represents the radius as a function of time. O The function represents the radius as a function of volume. The function represents the time as a function of volume. The function represents the volume as a function of the radius.

A spherical balloon is being inflated. The radius of the balloon is increasing at the rate of 6 cm/s. (a) Find a function f that models the radius as a function of time t, in seconds. f(t) = (b) Find a function g that models the volume as a function of the radius r, in cm. g(r) = %3D (c) Find g o f. gof = What does this function represent? O The function represents the volume as a function of time. The function represents the radius as a function of time. O The function represents the radius as a function of volume. The function represents the time as a function of volume. The function represents the volume as a function of the radius.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.6: Optimization

Problem 7E: Marine Fishery One class of models for population growth rates in marine fisheries assumes that the...

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A forest fire leaves behind an area of grass burned in an expanding circular pattern. If the radius of the circle of burning grass is increasing with time according to the formula r(t)=2t+1 , express the area burned as a function of time, t (minutes).
Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.
Marine Fishery One class of models for population growth rates in marine fisheries assumes that the harvest from fishing is proportional to the population size. For one such model, we have G=0.3n(1n2)0.1n Here G is the growth rate of the population, in millions of tons of fish per year, and n is the population size, in millions of tons of fish. a.Make a graph of G versus n. include values of n up to 1.5 million tons. b.Use functional notation to express the growth rate if the population size is 0.24 million tons, and then calculate that value. c. Calculate G1.42 and explain in practical terms what your answer means. d.At what population size is the growth rate the largest?