The number -3 written as a logarithm with a base of 2 is log₂(0.125) or log₂(1/8)
<h3>What are logarithms?</h3>
As a general rule, logarithms are mathematical expressions that are written in the form log(x) or ln(x), for natural logarithms
<h3>How to rewrite the number as a logarithm?</h3>
The number is given as:
x = -3
The base of the logarithm is given as:
Base = 2
To rewrite the given number as a base of 2, we take the exponent of the number where the base is 2
This is represented as:
Number =2^-3
Apply the power rule of indices
Number =1/2^3
Evaluate the exponent
Number = 1/8
Evaluate the quotient
Number = 0.125
Hence, when the number -3 is rewritten as a logarithm with base 2, the equivalent logarithm expression is log₂(0.125) or log₂(1/8)
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DB/dt = 1/5(100 - B)
5/(100 - B) dB = dt
-5 ln (100 - B) = t + C
Since B(0) = 20, then
-5 ln (100 - 20) = C
i.e. C = -5 ln 80
Thus -5 ln (100 - B) = t - 5 ln 80
or t = 5 ln 80 - 5 ln (100 - B) = 5 ln (80 / (100 - B))
When the weight = 40 grams
t = 5 In (80 / 100 - 40) = 5 In (80 / 60) = 5 ln (4/3) = 1.438 days
Rate of weight gain = 40 / 1.438 = 27.8 grams per day
When the weight = 70 grams
t = 5 ln (80 / 100 - 70) = 5 ln (80 / 30) = 5 ln (8/3) = 4.9 days
Rate of weight gain = 70/4.9 = 14.27 grams per day.
Therefore, the duck gains weight faster when it weighs 40 grams.
Answer:
Step-by-step explanation:
Mn
Answer:
107
Step-by-step explanation:
A circle is 360 degrees, so subtract 53,110, and 90 (right angle) from that.
Answer:
2434.235983
356794.4755
14.5
Step-by-step explanation:
Let's start by finding the effective rate
.054/12= .0045
and then the payment
There are two ways to find the unpaid balance (we also call this the oustanding loan balance). For this question (because all payments are equal) I am going to use the prospective method. The prospective method states that the outstanding loan balance is just the present value of the remaining payments
If 10 years have passed there are 20*12 payments and so we just need to find the present value of that
2.) We have the new loan amount (356794.4755) and so now we just need to calculate how long it will take it pay it off at a different rate
new effective rate: .024/12 = .002
