---
title: "A sample of an unknown radioactive isotope decays over time. The activity \\(A\\) of the sample as a function of time \\(t\\) is measured and plotted in the graph shown. Based on the graph, which of the following is the best estimate of the initial number of radioactive nuclei in the sample at \\(t = 0\\text{ s}\\)?"
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url: "https://nerd-notes.com/ubq/116538/"
date_modified: "2026-08-04T05:02:29+00:00"
---

# A sample of an unknown radioactive isotope decays over time. The activity \(A\) of the sample as a function of time \(t\) is measured and plotted in the graph shown. Based on the graph, which of the following is the best estimate of the initial number of radioactive nuclei in the sample at \(t = 0\text{ s}\)?

A sample of an unknown radioactive isotope decays over time. The activity \(A\) of the sample as a function of time \(t\) is measured and plotted in the graph shown. Based on the graph, which of the following is the best estimate of the initial number of radioactive nuclei in the sample at \(t = 0\text{ s}\)?

![A quantitative line graph of activity versus time. The horizontal axis is labeled time t (s) with major tick marks at 0, 100, 200, 300, and 400. The vertical axis is labeled activity A (10^8 Bq) with major tick marks at 0, 1.0, 2.0, 3.0, and 4.0. A smooth decreasing exponential decay curve starts at (0, 4.0), passes through (100, 2.0), (200, 1.0), (300, 0.5), and terminates at (400, 0.25). Light rectangular grid lines extend from all tick marks across the plotting region. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785819749-6Ooyow.jpg)

- **A.** \(4.0 \times 10^{10}\)
- **B.** \(5.8 \times 10^{10}\)
- **C.** \(1.2 \times 10^{11}\)
- **D.** \(2.3 \times 10^{11}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116538/*