# The half-life of a certain substance is 3.6 days. How long will it take for 20 g of the substance to decay to 7 g?

More specifically, you will have

Since the numbers don't allow for a quick calculation, your tool of choice will be the equation

Here

This will be equivalent to

Plug in your values to find

I'll leave the answer rounded to two sig figs, but keep in mind that you only have one sig figs for the initial mass of the sample and for the mass that remains undecayed.

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To find the time it takes for 20 g of the substance to decay to 7 g using the half-life formula, use the formula: [N = N_0 \times (0.5)^{\frac{t}{T_{\text{1/2}}}}]

Where:

- (N) is the final amount (7 g),
- (N_0) is the initial amount (20 g),
- (T_{\text{1/2}}) is the half-life (3.6 days),
- (t) is the time.

Rearrange the formula to solve for (t): [t = T_{\text{1/2}} \times \log_2\left(\frac{N}{N_0}\right)]

Plugging in the values: [t = 3.6 \times \log_2\left(\frac{7}{20}\right)]

Calculate (t): [t \approx 5.35 \text{ days}]

So, it will take approximately 5.35 days for 20 g of the substance to decay to 7 g.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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