Terri’s teacher gives her the equation 3(5)^x=127-2x, and tells her that she will not know how to solve it algebraically. Explain how Terri could use a graph to solve the equation. Find the value of x to the nearest tenth.

3(5^x) is an exponential function. and which rise very fast

y = 127 - 2x is a line Which decrease wçith a 2 slope f(0) = 127

3.5^2 = 75 and 3.5^3 = 375

I guess the intersection will be between 2and 3

lets put both the functions in a graph calculator

window:

x between 2 and 3

y between 75 and 127

I have an intersection between 2 and 3

use the "table" of the calculator

we can see that the intersection is between 2.3 and 2.4

try again

range:

start:2.3

end 2.4

intersection is in [2.3;2.31]

lets say it’s 2.305

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