In a lab experiment 8 grams of acid were produced in 28 minutes and 17 grams in 47 minutes. Let g be the number of grams and m be the number of minutes. Find a linear equation that you could use to calculate g for any number of minutes.

g = m t + b

m = (17-8)/(47-28) = .4737
so
g = .4737 t + b

8 = .4737 (28) + b
so
b = -5.263
so
g = 0.4737 t - 5.263

To find a linear equation that relates the number of grams produced (g) to the number of minutes (m), we can use the given data points: (8 grams, 28 minutes) and (17 grams, 47 minutes).

First, let's calculate the rate of acid production by finding the change in grams (∆g) and the change in minutes (∆m) between the two data points:
∆g = 17 grams - 8 grams = 9 grams
∆m = 47 minutes - 28 minutes = 19 minutes

Next, we can calculate the rate of acid production per minute, which is the slope (m) of the linear equation:
m = ∆g / ∆m = 9 grams / 19 minutes

Now that we have the slope, we can use either of the given data points to calculate the y-intercept (b) of the linear equation. Let's use the point (8 grams, 28 minutes) to find b:
g = m * m + b
8 grams = (9 grams / 19 minutes) * 28 minutes + b

Simplifying:
8 grams = (252 grams / 19 minutes) + b
8 grams - (252 grams / 19 minutes) = b

Now, we have the slope (m) and the y-intercept (b) to form the linear equation:
g = (9 grams / 19 minutes) * m + (8 grams - (252 grams / 19 minutes))

Simplifying further:
g = (9 / 19) * m + (152 / 19)
g = (9m + 152) / 19

Therefore, the linear equation that can be used to calculate g for any number of minutes is:
g = (9m + 152) / 19