Question

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.

Answer 1

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