what would 6(1/3) be equal to? I'm currently doing Exponential Growth and Decay, but I don't quite understand how to do this one....
The problem is y=6(1/3) exponent x
and it goes from exponent 1-5...
if the exponent is 2, then 6(1/3) exponent 2 would be equal to .66666666.....?
6 x (1/3) = 2
6 x (1/3)^2 = 6/9 = 2/3
etc.
what would 2/3 be as a decimal?
2/3= 0.6666
All terms after the first will be repeating decimals. The third term is 2/27 = 0.07407407...and the fourth is 2/81 = 0.024691358024601358024...
It is easier to write them as fractions.
Yes but the only thing is that I then have to graph it as a function...
To find the value of 6(1/3) raised to different exponents, we need to understand how exponentiation works.
In this case, 6(1/3) means taking the cube root of 6. The cube root of a number is the value that, when multiplied by itself three times, gives the original number. So, to find the cube root of 6, we need to find a number that, when multiplied by itself three times, equals 6.
To make it easier to understand, let's rewrite the expression as:
y = 6^(1/3)^x
Now, let's evaluate it for different values of x.
For x = 1:
y = 6^(1/3)^1 = 6^(1/3) = ∛6 ≈ 1.817
For x = 2:
y = 6^(1/3)^2 = 6^(2/3) = (∛6)^2 ≈ (1.817)^2 ≈ 3.309
Similarly, you can find the values for x = 3, x = 4, and x = 5 by multiplying the cube root of 6 by itself.
These calculations help us understand that raising 6^(1/3) to different exponents is equivalent to taking the cube root of 6 and then raising it to the desired exponent.