The probability, P, in percent, that a person will respond to a certain ad can be modelled by the equation P(n)=1-2^(-0.05n), where n is the number of days since the ad began on tv. After how many days is the probability greater than 20%?

my work:
0.20=1-2^(-0.05n)

then i solved for n, but i got a negative number.. what is wrong with my equation that i made and why

Your equation is correct, but it seems like there was an error in the way you solved for n. Let me guide you through the correct steps.

Starting with your equation:

0.20 = 1 - 2^(-0.05n)

Let's isolate the exponential term by subtracting 1 from both sides:

0.20 - 1 = -2^(-0.05n)

Now, let's simplify the left side:

-0.80 = -2^(-0.05n)

To eliminate the negative sign, we can multiply both sides by -1:

0.80 = 2^(-0.05n)

Next, let's convert the exponential equation to a logarithmic form:

log base 2 (0.80) = -0.05n

Now, we can solve for n by dividing both sides by -0.05:

n = (log base 2 (0.80)) / -0.05

When you evaluate this expression on a calculator or using logarithmic tables, you should get a positive value for n.

If you got a negative number, it's possible that you made a mistake in the calculations or used the wrong signs. Double-check your calculations and ensure that you are using the correct logarithmic base (base 2 in this case).