Final answer:
After 5 half-lives, there will be approximately 5.469 grams of the radioactive isotope remaining.
Step-by-step explanation:
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. To find out how much will be left after 5 half-lives, we need to calculate the remaining mass after each half-life and then multiply it by 0.5 for each subsequent half-life.
Starting with 175 grams, after 1 half-life, half of the initial mass will remain: 175 * 0.5 = 87.5 grams.
After 2 half-lives, half of the mass remaining after the first half-life will remain: 87.5 * 0.5 = 43.75 grams.
Continuing this pattern, after 3 half-lives: 43.75 * 0.5 = 21.875 grams.
After 4 half-lives: 21.875 * 0.5 = 10.9375 grams.
Finally, after 5 half-lives: 10.9375 * 0.5 = 5.46875 grams.