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(b) Graph this function for 0≤t≤100. Choose the correct graph below.

(b) Graph this function for 0≤t≤100. Choose the correct graph below.-example-1
(b) Graph this function for 0≤t≤100. Choose the correct graph below.-example-1
(b) Graph this function for 0≤t≤100. Choose the correct graph below.-example-2
User Hobhouse
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1 Answer

18 votes
18 votes

Part b.

This function represents a decay. Thus the values of A(t) must decrease with the increase of time t.

So, only graphs C and D are eligible answers.

Also, we are informed that the initial amount present is 800g, which can be obtained when making t = 0 in the expression that defines the function.

Therefore, for t = 0, we must have A(t) = 800. This means the graph crosses the vertical axis at A(t) = 800.

Thus, only option C is correct:

In order to know the half-life of this isotope, we can identify the point on the graph for which

A(t) = A(0)/2 = 800/2 = 400

Observing the graph, we can see that this happens for t between 20 and 30 years, but closer to 20:

Therefore, estimating the half-life of this isotope, the only possible answer is:

about 24.03 years (option C)

(b) Graph this function for 0≤t≤100. Choose the correct graph below.-example-1
(b) Graph this function for 0≤t≤100. Choose the correct graph below.-example-2
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