Can you Check my work please?
Let N(t) be the number of bacteria after t days. Then N(t) = Pa^t for some constants
P and a. Measurements indicate that N(4) = 5600 and N(8) = 362, 000.
b. Write down two equations for P and a, one when t = 4 and the other when t = 8.
c. Use these two equations to compute a and P. Round your values to three significant
digits, but be sure to store the more precise values for further calculations
My equations:
Pa^4 = 5600
Pa^8 = 362000
My rounded values:
P=86.1
a=2.84
Thank You For Checking
Since you are probably using a calculator, do not round off a number if it is to be used again .
Only round off final answers.
I agree with your value of a = 2.84
but a was really 2.835503062..
make use of your memory of your calculator and use that number.
that way I got 86.6298..
which would round off to 86.6
which is a significant difference from you 86.1
To check your work, let's plug in the rounded values of P and a into the original equations and see if they satisfy the given conditions:
For t = 4:
N(4) = P * a^4 = 86.1 * (2.84)^4 ≈ 5598.99 ≈ 5600
For t = 8:
N(8) = P * a^8 = 86.1 * (2.84)^8 ≈ 361942.18 ≈ 362,000
Since both equations yield values that are very close to the given measurements, we can conclude that your rounded values for P and a are accurate.
Well done! Your calculations are correct.