The half life of carbon-14 is 5,730 years, assuming you start with 100% of carbon-14, what is the expression for the percent, p(t), of carbon-14 that remains in an organism that is t years old and what is the percent of carbon-14 remaining (rounded to the nearest whole percent) in an organism estimated to be 20,000 years old?
hint: the exponential equation for half life s p(t)=ao(0.5)^t/h, where p(t) is the percent of carbon-14 remaining, ao, is the initial amount (100%), t is age of organism in years, and h is the half life.
a. p(t)=100(0.5)^5,730t, 29% remaining
b. p(t)=100(0.5)^5,730/t, 91% remaining
c. p(t)= 5,730(0.5)^100t, 5,710 remaining
d. p(t)=100(0.5)^t/5,730, 9% remaining
answer: c.similar figures must have the same shape and the same size.
two figures are called similar if they have the same shape that is the ratio of their corresponding edges are in same proportion,
but it is not essential that they must have the same size.
for example, if we have two right triangles,
first having sides 3, 4, 5 and second having sides 9, 12, 15,
since they are similar because their sides are in the same proportion,
also, in the case of triangles size is called area of the triangle,
the area of first triangle is 6 square unit, while second triangle has the area 54 square unit,
6 ≠ 54,
thus, both triangle have the different sizes.
⇒ third option is incorrect.
parallel lines have the same slope this is why they never intersect each other ⇒ first option is correct.
two figures are called congruent when they have same size and same shapes ⇒ second option is correct.
in rotation a figure is rotated around a point ⇒ fourth option is correct.