Question

work out the value of y when x = 4 30 points

Answer 1

Answer:

y = 54/25 when x = 4.

Step-by-step explanation:

y is given by the equation:

$\displaystyle y = p\times q^{x-1}$

Where p and q are numbers.

We are also given that when x = 1, y = 10 and when x = 6, y = 0.7776.

And we want to determine the value of y when x = 4.

Since y = 10 when x = 1:

$\displaystyle (10) = p\times q^{(1)-1}$

Simplify:

$10 = p \times q^0$

Any number (except for zero) to the zeroth power is one. Hence:

$p=10$

Thus, our equation is now:

$y = 10\times q^{x-1}$

When x = 6, y = 0.7776. Thus:

$(0.7776) = 10\times q^{(6)-1}$

Simplify and divide both sides by ten:

$\displaystyle 0.07776 = q^5$

Take the fifth root of both sides:

$\displaystyle q = \sqrt[5]{0.07776}$

Use a calculator. Hence:

$\displaystyle q = \frac{3}{5} = 0.6$

Our completed equation is:

$\displaystyle y = 10\times \left(\frac{3}{5}\right)^{x-1}$

Then when x = 4, y equals:

$\displaystyle \begin{aligned} y &= 10\times \left(\frac{3}{5}\right)^{(4)-1} \\ \\ &= 10\times \left(\frac{3}{5}\right)^3 \\ \\ &= 10\times \left(\frac{27}{125}\right) \\ \\ &= \frac{54}{25}\end{aligned}$