**(a)** Fit a cubic polynomial to the following data, and make a plot that shows the data as dots and the cubic fit as a smooth curve.

In [9]:

```
xdata = [-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0];
ydata = [3.41 3.19 2.57 2.44 1.90 1.66 1.17 1.46 1.07 1.44 2.28];
```

**(b)** Write out the polynomial in the form $P(x) = c_0 + c_1 x + c_2 x^2 + c_3 x^3$ with the coefficients specified as numeric values with three digits.

In [ ]:

```
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**(a)** Given the following experimental measurements of alpha-particle emission of a radioactive substance, fit an exponential function $y = c \exp(a t)$ to the data using least squares. Make a plot that shows the data as dots and the exponential fit as a smooth curve. What are the values of $c$ and $a$?

In [8]:

```
tdata = [0 4 8 12 16 20 24 28 32 36 40 44 48]; # time in hours
ydata = [69 64 54 41 44 34 26 29 18 22 18 19 11]; # alpha particle emission rate
```

Out[8]:

**(b)** What is the substance's half-life? (i.e. the time $t$ for which $y(t)/y(0) = 1/2$)

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**(a)** Fit a power-law curve $y = c t^a$ to the following data, and make a plot showing the datapoints as dots and the fit as a smooth curve.

In [11]:

```
tdata = [ 2 3 4 5 6 7 8 9 10];
ydata = [12.7 11.2 8.99 8.62 8.12 8.47 7.39 7.24 6.99];
```

**(b)** Write out the least-squares power-law fit $y = c x t^a$ with $c$ and $a$ specified as numeric values with three digits.

In [ ]:

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**(a)** The following data represent measurements of blood concentration of a drug after intravenous injection as a function of time. Fit a function of the form $y = c \, t \, e^{at}$ to the data using least squares. Make a plot that shows the data as dots and the exponential fit as a smooth curve.

In [12]:

```
tdata = [4 8 12 16 20 24]; # time in hours
ydata = [21 31 25 21 15 16]; # concentration in ng/ml
```

Out[12]:

**(b)** Write out the model $y = c \, t \, e^{at}$ with numeric values specified to three digits.

In [ ]:

```
```

**(c)** Based on the model, at what time do you expect the concentration to reach 5 ng/ml?

In [ ]:

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```