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 ≈ 3.561

Therefore, approximately after 3.561 years, 10 grams of the radioactive material will remain.