Please help with number 42 and 43. the 500-m speed-skating eventas a function of the number of years since 1994, andpredict the winning time in 2018, if we assume the de-crease in time is(a) Linear(b) Exponential42. In yeart = 0 a lake is estimated to have about 3500trout in it. Ten years later, at t = 10, the population oftrout is believed to be about 1700.(a) Write a formula for the size of the population P asa function of year t if we assume the decrease islinear. What is the rate of change, in fish per year,of the function over the ten-year period?(b) Write a formula for the size of the population P asa function of year t if we assume the decrease isexponential. What is the percent rate of change, inpercent per year, of the function over the ten-yearperiod?(c) Graph the two functions on the same coordinatesystem. Indicate the points at t = 0 and t = 10.43. Cocoa production'5 is shown in Table 4.8 for the worldand the Ivory Coast, in millions of tons, as a function ofthe number of years since 2000. In each case, determineif production is better modeled with a linear or an ex-ponential function and find a formula for the function.Table 4.8Years since 20000.134World cocoa production3.13.8754.8446.0557.568Ivory Coast cocoa production1.31.341.381.421.46

Name: Please help with number 42 and 43. the 500-m speed-skating eventas a f
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Description: Please help with number 42 and 43. the 500-m speed-skating eventas a function of the number of years since 1994, andpredict the winning time in 2018, if we assume the de-crease in time is(a) Linear(b) Exponential42. In yeart = 0 a lake is estimated t

Answered: (b) Exponential 42. In yeart = 0 a lake…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please help with number 42 and 43.

the 500-m speed-skating event
as a function of the number of years since 1994, and
predict the winning time in 2018, if we assume the de-
crease in time is
(a) Linear
(b) Exponential
42. In yeart = 0 a lake is estimated to have about 3500
trout in it. Ten years later, at t = 10, the population of
trout is believed to be about 1700.
(a) Write a formula for the size of the population P as
a function of year t if we assume the decrease is
linear. What is the rate of change, in fish per year,
of the function over the ten-year period?
(b) Write a formula for the size of the population P as
a function of year t if we assume the decrease is
exponential. What is the percent rate of change, in
percent per year, of the function over the ten-year
period?
(c) Graph the two functions on the same coordinate
system. Indicate the points at t = 0 and t = 10.
43. Cocoa production'5 is shown in Table 4.8 for the world
and the Ivory Coast, in millions of tons, as a function of
the number of years since 2000. In each case, determine
if production is better modeled with a linear or an ex-
ponential function and find a formula for the function.
Table 4.8
Years since 2000
0.
1
3
4
World cocoa production
3.1
3.875
4.844
6.055
7.568
Ivory Coast cocoa production
1.3
1.34
1.38
1.42
1.46

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Given - In year t = 0 a lake is estimated to have about 3500 trout in it. Ten years later, at t = 10 , the population of trout is believed to about 1700.

To find -

Write the formula for the size of the population P as a function of year t if we assume the decrease is linear . What is the rate of change, in fish per year, of the function over the ten-year period?
Write the formula for the size of the population P as a function of year t if we assume the decrease is exponential . What is the rate of change, in percent per year, of the function over the ten-year period?
Graph the two functions on the same coordinate system . Indicate the points at t = 0 and t = 10.

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