See below PLEASE at ********

If computing N(t) = Pa^t where P=642.035376 and a = 2.900129566 (both are stored in calculator), to what extent should the values of N(5), N(7) and N(9) be rounded? and why?

Note:
N(5)= 131,718
N(7)= 1,107,849
N(9)= 9,317,847

algebra - bobpursley, Sunday, November 6, 2011 at 3:18pm
Hmmmm. How many sig digits are in t? ONE? 5,7,9?

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So is the answer is ONE because t (even though it's an exponential and not a factor) only has one sig fig?
I thought it would be the 9 sig figs of P that was the lowest

I am trying to figure out t. If it is a counting number, it is infinitely sigificant, and you are correct on P. If t is a measured number, then it only has one sig digit.

I have no idea the nature of t.

N(t) refers to the number of bacteria after t days.

Does that help? does the exponent t still me answers should be rounded to one sig fig?
N(t) = Pa^t

t in days... is there a number such as t=1.345 days? (yes). So, I would treat t as one sig digit.

n(5)=100,000
n(7)=1,000,000
n(9)=9,000,000

To determine the extent to which the values of N(5), N(7), and N(9) should be rounded, you need to consider the number of significant figures in the inputs (P and a) and the resulting calculations.

In this case, the values of P and a are given with the following significant figures:
P = 642.035376 (9 significant figures)
a = 2.900129566 (10 significant figures)

The general rule for multiplication or division is that the result should have the same number of significant figures as the input with the fewest significant figures. In this case, P has 9 significant figures, which is fewer than the 10 significant figures in a. Therefore, the calculated results should be rounded to the same precision as P.

Now let's calculate N(5), N(7), and N(9) using the given formula:
N(5) = P * a^5 = 642.035376 * (2.900129566)^5 ≈ 642.035376 * 397.476468 ≈ 255,380 (rounded to the same precision as P, which is one decimal place)

N(7) = P * a^7 = 642.035376 * (2.900129566)^7 ≈ 642.035376 * 1,152.186364 ≈ 739,716 (rounded to the same precision as P, which is one decimal place)

N(9) = P * a^9 = 642.035376 * (2.900129566)^9 ≈ 642.035376 * 3,350.837018 ≈ 2,153,236 (rounded to the same precision as P, which is one decimal place)

Therefore, the values of N(5), N(7), and N(9) should be rounded to one decimal place (or to the same precision as P) because P has the fewest significant figures among the inputs. The exponent (t) in the function does not affect the number of significant figures to round to.