Show all work. No decimal answers, except in problem 6.
Simplify:
5^0a^6b^3
(-4)^-1
(2a^4y^3)^3
()-2
Simplify the expression. Write your answer in scientific notation.
(4 x 108)(8.2 x 10-2)
The amount of bacteria in a raw piece of meat doubles every 3 hours. If the meat initially contains 135 ounces of bacteria, how much bacteria will be in the meat after 15 hours?
What is the value of 12a-4b-3 for a = 2 and b = -1?
Is the rule y = 2x3 represent an exponential function? Explain. (2 pts.)
5^0a^6b^3
----------------- anything^0 = 1
(-4)^-1
--------------------------- 1/-4 = -1/4
(2a^4y^3)^3
2^3 =8
so 8 a^12 y^9
()-2
means nothing to me at all
Simplify the expression. Write your answer in scientific notation.
(4 x 108)(8.2 x 10-2)
PROOF READ
I think you mean 4*10^8 * 8.2*10^-2
= 32.8 * 10^6
= 3.28 *10^7
BUT you typed 4 all alone not 4.0 or 4.00
that means ONE significant figure
so 3 * 10^7
answer depends on your typing errors
The amount of bacteria in a raw piece of meat doubles every 3 hours. If the meat initially contains 135 ounces of bacteria, how much bacteria will be in the meat after 15 hours?
==================
doubles five times
135 * 2^5 = 135 * 32
What is the value of 12a-4b-3 for a = 2 and b = -1?
------------ 12(2) -4(-1) -3 = 24 + 4 -3 = 25
Is the rule y = 2x3 represent an exponential function? Explain. (2 pts.)
--------------- NOT the way you TYPED it
if you mean
y = 2 x^3 then it is exponential, x to the exponent 3
1) Simplify: 5^0a^6b^3
To simplify this expression, we can use the rule that any number raised to the power of 0 is equal to 1. Therefore, 5^0 is equal to 1. The other terms, a^6 and b^3, remain unchanged.
Final simplified expression: 1 * a^6 * b^3 = a^6b^3
2) Simplify: (-4)^-1
To simplify this expression, we can use the rule that any number raised to the power of -1 is equal to its reciprocal. Therefore, (-4)^-1 is equal to 1/-4 or -1/4.
Final simplified expression: -1/4
3) Simplify: (2a^4y^3)^3
To simplify this expression, we need to apply the power rule, which states that when raising a power to another power, we multiply the exponents. Therefore, (2a^4y^3)^3 is equal to 2^3 * (a^4)^3 * (y^3)^3.
Simplifying further, we have 8a^(4*3) * y^(3*3) = 8a^12y^9
Final simplified expression: 8a^12y^9
4) Simplify: ()
The expression is missing, so we cannot simplify it without knowing the contents of the parentheses.
5) Simplify the expression: (4 x 10^8)(8.2 x 10^-2)
To simplify this expression, we can multiply the numerical parts separately and add the exponents of 10.
(4 x 8.2) x (10^8 x 10^-2) = 32.8 x 10^(8 - 2) = 32.8 x 10^6
Final simplified expression: 3.28 x 10^7
6) The amount of bacteria in a raw piece of meat doubles every 3 hours. If the meat initially contains 135 ounces of bacteria, how much bacteria will be in the meat after 15 hours?
To solve this problem, we can use the concept of exponential growth. Since the amount of bacteria doubles every 3 hours, we can divide the total time (15 hours) by the time it takes for the bacteria to double (3 hours).
15 / 3 = 5
So, the bacteria will double 5 times over the 15-hour period. Starting with an initial amount of 135 ounces, after each doubling, the amount of bacteria will be multiplied by 2.
First doubling: 135 * 2 = 270 ounces
Second doubling: 270 * 2 = 540 ounces
Third doubling: 540 * 2 = 1080 ounces
Fourth doubling: 1080 * 2 = 2160 ounces
Fifth doubling: 2160 * 2 = 4320 ounces
Final answer: After 15 hours, there will be 4320 ounces of bacteria in the meat.
7) What is the value of 12a^-4b^-3 for a = 2 and b = -1?
We can substitute the given values of a and b into the expression and simplify it.
12(2)^-4(-1)^-3
Using the rule that a negative exponent is equivalent to 1 divided by the positive exponent, we can rewrite the expression:
12/2^4 * 1/(-1)^3
Simplifying further:
12/16 * 1/(-1)
Multiplying and dividing:
12/-16 = -3/4
Final answer: The value of 12a^-4b^-3 for a = 2 and b = -1 is -3/4.
8) Is the rule y = 2x^3 represent an exponential function? Explain.
No, the rule y = 2x^3 does not represent an exponential function. An exponential function has the form y = ab^x, where the base (b) is a constant. In this case, the equation y = 2x^3 represents a polynomial function, specifically a cubic function, because the highest power of x is 3. The coefficient 2 is not a constant raised to the power of x, as expected in an exponential function.