The correct expression for A in the given problem is option C:
![A=1.44^((-1.2))](https://img.qammunity.org/2022/formulas/mathematics/high-school/c73hkzcno3ry4p0bxotb7nu9i859f8aqxs.png)
Let's rewrite
as
and then compare it to the given options:
![1.44^(-1.2 x)=A^x](https://img.qammunity.org/2022/formulas/mathematics/high-school/p7gc5v4ajhvink6km8ff6gycmofus8tkqp.png)
Now, let's express 1.44 in terms of A:
![A=1.44^((-1.2))](https://img.qammunity.org/2022/formulas/mathematics/high-school/c73hkzcno3ry4p0bxotb7nu9i859f8aqxs.png)
Now, let's substitute this value of A back into the original equation:
![1.44^(-1.2 x)=\left(1.44^((-1.2))\right)^x](https://img.qammunity.org/2022/formulas/mathematics/high-school/wm230mik3zurswq7h3ahyq23unoy6n10wk.png)
Now, compare this expression with the provided options:
Certainly! Let's rewriteB.
as Ax:
A=1.44^{(-1.2)} - AX
Now, let's take the natural logarithm (ln) of both sides to simplify the exponent
In (¹.⁴⁴¹.²ˣ) - In (Ax)
Using the property In ⁽ᵃᵇ⁾ -b In(a) we can bring down the exponent:
1.2xln(1.44)=xln(A)
Now, solve for A: n(A)= 1.2ln(1.44/1)
ln(A)=0.1392
Now, exponentiate both sides to solve for A:
A=e 0.1392
So, A is approximately equal to:
A≈1.1496
Therefore, when you rewrite ¹.⁴⁴¹.²ˣ as ᴬ, the value of A is approximately 1.1496.