Acertain radioactive isotope decays at a rate of 0.3% annually. determine the half-life of this isotope, to the nearest year

This could be rephrased as:

You start with 100 grams of a substance.  One year later you have 70 grams.  What is the half-life?

We need this formula:

half-life = (time * natural log (2)) / natural log (beginning amount / ending amt)

half-life = (1 year * .69315) / natural log (100 / 70)

half-life = (.69315) / 0.35667494396

half-life = 1.9433661145 years

Rounding to nearest year half-life = 2 years

Sourse: https://www.1728.org/halflif2.htm

(See problem 3)

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.