The monthly revenue of the business grows by 8%, monthly
<h3>What is an exponential function?</h3>
An exponential function is any function that has its constant raised to the power of an argument.
An exponential function is represented as:
Where:
- a represents the initial value
- b = 1 + r; r represents the rate
From the table we have the following ordered pair
(x,y) = {(0,72000) (3,90000)}
So, we have:
Divide both sides by 72000
Take the cube roots of both sides
![b=\sqrt[3]{1.25}](https://tex.z-dn.net/?f=b%3D%5Csqrt%5B3%5D%7B1.25%7D)
Recall that:
So, we have:
Subtract 1 from both sides
Express as percentage
Hence, the monthly revenue of the business grows by 8%, monthly
Read more about exponential functions at:
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Formulas tab > in the Function Library group, click Lookup & Reference button, select VLOOKUP. Type A3 in the Lookup_value argument box. Type Abbreviation in the Table_array argument box. Type 2 in the Col_num argument box. Type False in the Rang_lookup box. Click OK, is this what you were looking for?
The smallest prime number of p for which p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
<h3>What is the smallest prime number of p for which p must have exactly 30 positive divisors?</h3>
The smallest number of p in the polynomial equation p^3 + 4p^2 + 4p for which p must have exactly 30 divisors can be determined by factoring the polynomial expression, then equating it to the value of 30.
i.e.
By factorization, we have:
Now, to get exactly 30 divisor.
- (p+2)² requires to give us 15 factors.
Therefore, we can have an equation p + 2 = p₁ × p₂²
where:
- p₁ and p₂ relate to different values of odd prime numbers.
So, for the least values of p + 2, Let us assume that:
p + 2 = 5 × 3²
p + 2 = 5 × 9
p + 2 = 45
p = 45 - 2
p = 43
Therefore, we can conclude that the smallest prime number p such that
p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
Learn more about prime numbers here:
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B. 9*10^16 (because in question give it)
B. 3*10^9 (because answer to first question is divided by seconds in one year (365*24*60*60).
