A blob of a certain radioactive substance is decaying expone

A blob of a certain radioactive substance is decaying exponentially with respect to time. After 10 days, the mass is 8 grams. After 12 days, the mass is 6 grams. What will the mass of the blob be in 20 days? What is the half-life of the substance?

Note: Can you please list out the steps? Thanks!

Solution

we have two points ( 10,8 ) and ( 12 , 6 )

finding exponnetial model using these points

y = ab^x

8 = ab^10

6 = ab^12

dividing the two equations

b^2 = 6/8

b^2 = 3/4

b = 0.8660

a = 33.71

hence , equation is

y = 33.71 (0.8660)^x

where x is the number of days

mass of blog after 20 days

y = 33.71 ( 0.8660)^20

y = 2 grams

half life

33.71 /2 = 33.71 (0.8660)^x

x = 4.818

half life is 4.82 days