Answer:
y = 3 * 9^x
Step-by-step explanation:
To write an exponential function in the form y = ab that goes through the points (0, 3) and (2, 243), we need to find the values of a and b.
Let's start by using the point (0, 3). When x = 0, y = 3. Substituting these values into the exponential function equation, we get:
3 = ab^0
3 = a * 1
a = 3
Now, let's use the second point (2, 243). When x = 2, y = 243. Substituting these values into the exponential function equation, we get:
243 = 3b^2
To find the value of b, we can rewrite the equation as:
3b^2 = 243
Dividing both sides of the equation by 3, we have:
b^2 = 81
Taking the square root of both sides, we get:
b = ±9
Since we are looking for a positive value for b, we can take b = 9.
Therefore, the exponential function that goes through the points (0, 3) and (2, 243) is: y = 3 * 9^x
A computer designer has to build a computer which can executes 300 instructions and represents integers in
[tex] - {10}^{14} [/tex]
to
[tex] {10}^{14} [/tex]
lf one instruction is stored in the entire memory word, what is the maximum memory capacity this computer can occupy?
The computer can occupy a maximum of 1200 bytes of memory.
To determine the maximum memory capacity of a computer that can execute 300 instructions, we need to consider the representation of integers and the storage requirements for instructions.
If each instruction is stored in the entire memory word, it implies that each instruction occupies one memory word. Therefore, the number of instructions executed (300) directly corresponds to the number of memory words required.
The memory capacity of a computer is typically measured in bytes. However, since we are assuming each instruction occupies one memory word, we can consider the memory capacity in terms of memory words.
Hence, the maximum memory capacity this computer can occupy would be 300 memory words.
To convert this capacity into bytes, we need to know the size of a memory word. If we assume the computer uses a 32-bit word size, which is common in many systems, each memory word would consist of 4 bytes (32 bits / 8 bits per byte). Therefore, the maximum memory capacity in bytes would be:
300 memory words * 4 bytes per word = 1200 bytes.
for more such questions on memory
https://brainly.com/question/31399102
#SPJ8
what is the answer too (x^3.x^2)^4 divided by 3x^4
[tex]((x^3) * (x^2))^4[/tex] divided by [tex]3x^4[/tex]simplifies to[tex]x^{16/3[/tex]using the rules of exponents.
To simplify the expression[tex]((x^3) * (x^2))^4[/tex]divided by [tex]3x^4[/tex], we need to follow the rules of exponents.
First, let's simplify the numerator,[tex]((x^3) * (x^2))^4[/tex]. According to the exponent rule for multiplying powers with the same base, when we multiply two powers with the same base, we add their exponents. Applying this rule, we get[tex](x^{(3+2)})^4[/tex], which simplifies to [tex](x^5)^4.[/tex]
Next, we apply the exponent rule for raising a power to another power. When we raise a power to another power, we multiply the exponents. In this case, we have [tex](x^5)^4[/tex], which becomes [tex]x^{(5*4)[/tex] or [tex]x^{20.[/tex]
Now let's simplify the denominator, [tex]3x^4[/tex]. Since division is equivalent to multiplying by the reciprocal, we can rewrite the expression as [tex](x^{20})/(3x^4).[/tex]
To simplify this division, we use the exponent rule for dividing powers with the same base. According to this rule, when we divide two powers with the same base, we subtract their exponents. In this case, we have [tex]x^{20[/tex] divided by x^4, which gives us[tex]x^{(20-4)[/tex]or x^16.
Therefore, the simplified expression for [tex]((x^3) * (x^2))^4[/tex]divided by 3x^4 is[tex]x^{16/3.[/tex] This is the final answer, as the expression has been simplified as much as possible.
In summary,[tex]((x^3) * (x^2))^4[/tex]divided by 3x^4 simplifies to [tex]x^{16/3[/tex] using the rules of exponents.
For more question on divided visit:
https://brainly.com/question/30224866
#SPJ8
