SME
Historical Geology
The fossil record
Use this for “A trilobite lived 505–490 Ma and a brachiopod 497–480 Ma. When did a bed holding both form?”
Diagram
Oldest = the youngest first appearance = 400 Ma.
Youngest = the oldest last appearance = 380 Ma.
The bed formed in a 20-Myr window.
This is an example. Type your own values to start a new problem.
Afirst
Fossil A first appears
example · Ma
Aₗₐₛₜ
Fossil A last appears
example · Ma
Bfirst
Fossil B first appears
example · Ma
Bₗₐₛₜ
Fossil B last appears
example · Ma
told
Oldest possible age
worked out (not typed) · Ma
tyoung
Youngest possible age
worked out (not typed) · Ma
Δt
Window
worked out (not typed) · Myr
Formulas
told = min(Afirst, Bfirst)
400 = min(420, 400)
tyoung = max(Aₗₐₛₜ, Bₗₐₛₜ)
380 = max(380, 360)
Δt = told − tyoung
20 = 400 − 380
Assumptions
•
A bed holding both fossils formed while both lived, so its age lies inside both ranges.
•
The ranges come from dated sections elsewhere; each first appearance is the older age.
•
Ranges that never overlap are rejected: these fossils never lived at the same time.
Step-by-step
WE KNOW
Afirst = 420 Ma, Aₗₐₛₜ = 380 Ma, Bfirst = 400 Ma, Bₗₐₛₜ = 360 Ma
FIND
oldest possible age (told), youngest possible age (tyoung), window (Δt)
Step 1 · Find oldest possible age (told)
Use told = min(Afirst, Bfirst)
The bed is no older than the later of the two first appearances: the smaller age.
told = min(420, 400)
told = 400 Ma
Step 2 · Find youngest possible age (tyoung)
Use tyoung = max(Aₗₐₛₜ, Bₗₐₛₜ)
It is no younger than the earlier of the two last appearances: the larger age.
tyoung = max(380, 360)
tyoung = 380 Ma
Step 3 · Find window (Δt)
Use Δt = told − tyoung
The window is the stretch of time when both fossils lived.
Δt = 400 − 380
Δt = 20 Myr
Check
Put the numbers back in. Both sides should match.
400 = min(420, 400) ✓
380 = max(380, 360) ✓
20 = 400 − 380 ✓
Topic check
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