Question

2. The number of atoms of a particular chemical element is modelled by

the following function: y=600 x 3-* where x is the number of hours.
a) How many atoms of the element were there at the start?
b) Draw a graph for 0 c) At what time were there 150 atoms?

Answer 1

9514 1404 393

Answer:

a) 600

b) see below

c) 1.26 hours

Explanation:

a) The value of y when x=0 is the coefficient of the exponential term:

y = 600·3^(-0) = 600·1 = 600

There were 600 atoms to start.

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b) see attached for a graph

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c) The graph shows 150 atoms at t = 1.26, about 1.26 hours after the start of time counting.

If you want to find that value algebraically, substitute for y and solve for x. Logarithms are involved.

150 = 600·3^(-x)

150/600 = 3^(-x)

log(1/4) = -x·log(3)

x = -log(1/4)/log(3) = log(4)/log(3) ≈ 1.2618595

After about 1.26 hours, there were 150 atoms.