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4 years ago

15

Daniel is looking over some data regarding the temperatures of countries and how the temperature relates to the number of mosqui

toes. The data are represented by the exponential function f(x) = 2x, where x is the number of mosquitoes. Explain how he can convert this equation to a logarithmic function when the temperature is 64 degrees.

1 answer:

ludmilkaskok [199]4 years ago

7 0

64 = 2^x
log 64 = log 2^x = x log 2

Required logarithm function is log 64 = x log 2

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Solve the following using Substitution method<br> 2x – 5y = -13<br><br> 3x + 4y = 15

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$\huge \boxed{\mathfrak{Question} \downarrow}$

Solve the following using Substitution method

2x – 5y = -13

3x + 4y = 15

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$\left. \begin{array} { l } { 2 x - 5 y = - 13 } \\ { 3 x + 4 y = 15 } \end{array} \right.$

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

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Choose one of the equations and solve it for x by isolating x on the left-hand side of the equal sign. I'm choosing the 1st equation for now.

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$x=\frac{1}{2}\left(5y-13\right) \\$

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Multiply 3 times $\frac{5y-13}{2}\\$ .

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Add $\frac{15y}{2} \\$ to 4y.

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Add $\frac{39}{2}\\$ to both sides of the equation.

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Divide both sides of the equation by 23/2, which is the same as multiplying both sides by the reciprocal of the fraction.

$\large \underline{ \underline{ \sf \: y=3 }}$

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$x=\frac{5}{2}\times 3-\frac{13}{2} \\$

Multiply 5/2 times 3.

$x=\frac{15-13}{2} \\$

Add $-\frac{13}{2}\\$ to $\frac{15}{2}\\$ by finding a common denominator and adding the numerators. Then reduce the fraction to its lowest terms if possible.

$\large\underline{ \underline{ \sf \: x=1 }}$

The system is now solved. The value of x & y will be 1 & 3 respectively.

$\huge\boxed{ \boxed{\bf \: x=1, \: y=3 }}$

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