A bacteria culture grows with constant relative growth rate. The bacteria count was 2,560 after 4 hours and 81,920 after 8 hours.

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A: We can answer the question as below.

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A: the given function f(x)=x-12 on the interval 2,4

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A: To solve the following problem

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A: Given:   To determine: dy/dx using implicit differentiation.

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A: We need to evaluate integral.

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A: answer is in next step

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A: Given query is to find the solution of the differential equation.

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A: ∫02tanhx dx=∫02sinhxcoshxdxUsing formula ∫f'(x)f(x)dx = ln|f(x)| +cHere , f(x)=sinhx , f'(x)= coshx

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A: Here we have to integrate the given function.

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A: In this question , we can solve the system of equation by eliminating the variables .

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A: In polar coordinate r,θ,if  r is negativen then add π to the angle . Note : As per our Guidelines ,…

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A: Follow the procedure given below.

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A: Solving

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