This is an exponential equation that can be represented by the following:
f(x) = a(b)^x
In this case...
25143 = a(0.66)^3
25143 is the population after 3 hours.
3 is the amount of time in hours.
0.66 represents the percent of the population remaining after each hour (66% as there is a 34% decline each hour).
We must solve for a, which is the initial population.
First, simplify (0.66)^3 to 0.2874.
25143 = 0.2874a
Now divide both sides by 0.2874 to isolate a.
a = 87455
There were initially 87,455 people within the city. I wouldn't want to be in that place!
Dollars or cents
what is the question
The equation of
by maclaurin series is
.
The maclaurin series for f(x) is defined by the following formula:
--------------(1)
Where
is the i - th derivative of the function
If f(x) =
, then the formula of the i - th derivative of the function is:
----------------------(2)
Then,

Lastly, the equation of the trascendental function by Maclaurin series is:
---------------(3)
Hence,
The equation of
by maclaurin series is
.
Find out more information about maclaurin series here
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This is easy! Just use the point-slope form:

Plug in the values:
-1 - 4 = m(2 - (-3))
Combine like terms
-5 = 5m
Divide both sides by 6
m = 5/-5 or
m = -1
<u>Answer:</u>
a. the error is that he wrote 0.05 instead of 0.2
0.148835 ≈ 0.2
b.
0.2 = 2 × 0.1
0.2 = 2 × 10⁻¹
The mass is about 2 × 10⁻¹ kg