contestada

consider the model of exponential growth or decay given by A = A exp(kt). If k ________ the function models amount or size of a growing entity if k ________ the models amount size of a decaying entity'.

which answers are

a >0; <0
b =0;=/0
c >0; <0
d <0; <0

Respuesta :

lublana

Answer:

(a) >0;<0

Step-by-step explanation:

We are given that an exponential function

[tex]A=A_0e^{kt}[/tex]

We have to find the correct answer.

Differentiate w.r.t t

[tex]\frac{dA}{dt}=kA_0e^{kt}[/tex]

If k is positive

i.e k>0

Then, [tex]\frac{dA}{dt}=Positive >0[/tex]

Hence, the function is increasing.

When k is negative

i.e k<0

Then,[tex]\frac{dA}{dt}=negative<0[/tex]

Hence, the function is decreasing.

If k>0 the functions models amount or size of a growing entity if k<0 the models amount size of a decaying entity.

Option (a) is true.

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