Answer:
1. y-intercept is -1.
2. Exponential form is \(0.80^{4}=0.4096\).
3. 2.875
4. y = 0.873
Step-by-step explanation:
1. We have the function \(f(x) = -32 \times 2^{x-3} +3\).
Now as we know that y-intercept is the point where the line cuts y-axis i.e. x=0.
So, x=0 in the \(f(x) = -32 \times 2^{x-3} +3\) gives,
\(f(x) = -32 \times 2^{0-3} +3\)
i.e. \(f(x) = \frac{-32}{2^{3}}+3\)
i.e. \(f(x) = \frac{-32}{8}+3\)
i.e. \(f(x) = -4+3\)
i.e. \(f(x) = -1\)
So, the y-intercept of this function is -1.
2. We have, \(4=\log_{0.80}{0.4096}\)
As, \(a=\log_{b}c\) implies \(b^{a}=c\).
Therefore, \(4=\log_{0.80}0.4096\) implies \(0.80^{4}=0.4096\).
Hence, the exponential form is \(0.80^{4}=0.4096\).
3. We have to find the value of log(750).
As no base is given, we assume the base to be 10.
So, \(\log_{10}750\) = 2.875.
4. We have, \(y=\log_{40}{25}\)
Again using, As, \(a=\log_{b}c\) implies \(b^{a}=c\).
We have, As, \(y=\log_{40}25\) implies \(40^{y}=25\)
i.e. \(y \times \log40 = \log25\)
i.e. y = 0.87258905175
Rounding to nearest thousand gives y = 0.873.
