He amount of carbon-14 present in animal bones t years after the animal's death is given by p(t)equals=upper p 0 e superscript negative 0.00012097 tp0e−0.00012097t. how old is an ivory tusk that has lost 26% of its carbon-14?

t = 2489 years

Step-by-step explanation:

The equation you need for this is

where N is the amount AFTER the decomposition, N-sub-0 is the initial amount, k is the decomposition constant and t is time in years.

If we are told that the tusk LOST 26% of its carbon-14, that means 74% of it remains from the initial 100% it had.

Filling in:

Begin by dividing both sides by 100 to get a decimal of .74:

The goal is to get that t out of the exponential position in which it is currently sitting.  Do this by "undoing" the e.  Do THAT by taking the natural log of both sides because a natural log "undoes" an e.  This is due to the fact that the base of a natural log is e.  

The ln and the e disappear on the right side, leaving

ln(.74) = -.00012097t

Plug ln(.74) into your calculator to get

-.3011050928 = -.00012097t

t = 2489

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17