Sydney used 30 eggs with every 2 eggs making a cake. We can used simple division here.
30÷2 =15
Sydney made 15 cakes out of 30 eggs.
Solution: We know that formula for continuously compound interest is:
![A= P e^{rt}](https://tex.z-dn.net/?f=%20A%3D%20P%20e%5E%7Brt%7D%20%20)
Where A is the future amount $900 x 2 = $1800
P is the principal investment $900
e is the eular's constant
r is rate of interest 0.09
t is the time ( to be found)
Therefore we have:
![1800=900 \times e^{0.09 \times t}](https://tex.z-dn.net/?f=%201800%3D900%20%5Ctimes%20e%5E%7B0.09%20%5Ctimes%20t%7D%20%20)
![2=e^{0.09 \times t}](https://tex.z-dn.net/?f=%202%3De%5E%7B0.09%20%5Ctimes%20t%7D%20%20)
Taking natural log on both sides
![ln(2)=0.09 \times t](https://tex.z-dn.net/?f=%20ln%282%29%3D0.09%20%5Ctimes%20t%20)
![t=\frac{ln(2}{0.09}](https://tex.z-dn.net/?f=%20t%3D%5Cfrac%7Bln%282%7D%7B0.09%7D%20%20)
![t=7.702](https://tex.z-dn.net/?f=%20t%3D7.702%20%20)
Therefore it will take 7.702 years to double the amount
The value of x is from negative infinity to negative 3/7 and 29 to positive infinity.
<h3>What is inequality?</h3>
Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality equations are given below.
a) - 9x + 7 > 16 + 12x
b) 18 + 13x < 14x - 11
Then
a) - 9x + 7 > 16 + 12x
Solving for x, we have
21x < -9
x < -3/7
The value of x is less than the negative of 3/7.
b) 18 + 13x < 14x - 11
Solving for x, we have
x > 29
The value of x is greater than 29.
More about the inequality link is given below.
brainly.com/question/19491153
#SPJ1
21 + 15 = 36
36 x 3 = 108
Their father donated $108 to charity