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ss7ja [257]
3 years ago
11

In a certain town, the amount of sulfur oxide in the air, S, in tons, is related to the town’s population, P, in people. The rel

ationship is S2 = 1 10 P2 + 20P + 600 The town’s population is growing at a rate, with respect to time, of 10 people/month. At what rate, with respect to time, is the amount of sulfur oxide in the air changing, when the population is 100?
Mathematics
1 answer:
Lady bird [3.3K]3 years ago
8 0

Answer:

Change in sulfur oxide in the air = \frac{\textup{110010}}{\textup{S}}

Step-by-step explanation:

Data provided in the question:

Relation between the amount of sulfur oxide in the air and the population as:

S² = 110P² + 20P + 600

Population growth rate, \frac{\textup{dP}}{\textup{dt}}  = 10 people per month

Now,

change in sulfur oxide with time i.e \frac{\textup{dS}}{\textup{dt}}

differentiating the given relation with respect to time 't'

we have

2S\frac{\textup{dS}}{\textup{dt}} =  2\times110P\frac{\textup{dP}}{\textup{dt}}  + 20

at P = 100 and  \frac{\textup{dP}}{\textup{dt}}  = 10 people per month

we have

2S\frac{\textup{dS}}{\textup{dt}} = 2 × 110 × 100 × 10 + 20

or

2S\frac{\textup{dS}}{\textup{dt}} = 220020

or

\frac{\textup{dS}}{\textup{dt}} = \frac{\textup{220020}}{\textup{2S}}

or

Change in sulfur oxide in the air = \frac{\textup{110010}}{\textup{S}}

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