The amount A, of 70 grams of a certain radioactive material remaining after t years can be found by the equation A=70(0.62)^t. When will 10 grams remain?
just find t where
70*0.62^t = 10
.62^t = 1/7
t log.62 = log 1/7
t = log(1/7)/log(.62) = 4.07
To find the time when 10 grams remain, we can use the given equation A = 70(0.62)^t and substitute A with 10.
10 = 70(0.62)^t
Let's solve this equation for t.
Divide both sides of the equation by 70:
10/70 = (0.62)^t
Simplify the fraction:
1/7 = (0.62)^t
Now, let's take the logarithm of both sides of the equation, using base 0.62 to simplify the calculation:
log base 0.62 (1/7) = t
Using a calculator or logarithmic tables, we can determine the value of the logarithm:
t ā 3.561
Therefore, approximately after 3.561 years, 10 grams of the radioactive material will remain.