How do I find rate of change of the following(k)? and is this how you find y-intercept of exponential functions??

Question

1. f(x)=7^x and is the y-intercept 1 since x=0... 7^0=1, but how do you find the value of k? I know there is not k, which some are ya are confused in but k is not a variable, its something you have to find on a graph or of a exponential function?

One specfic question: How do you find the value of k without a graph so I can find the value of k in an exponential function problem?

1. f(x)=2^x/3 so 2^0=1 and so the y-intercept=1/3???
2. but how do you find the value of k(rate of change) the constant
3. f(x)=5(4)^x and x equals 0 you said so I plugged it in and got one, is this the y-intercept... but how do you find the value of k????
4. f(x)=5(9)^0}-2=3, so is 3 the y-intercept......

Please help!

Answer 1

Without a precise definition of k, we cannot answer the question. Some exponential functions have the form

f(x) = Ab^kx

where A, b, and k are constants. Could this be what they are asking for in your assignment? If so, then k is the coefficient in front of x in the exponential function.

Examples:

f(x) = 5 (2)^3x ⇒ k = 3

g(x) = 10 (5)^x/7 ⇒ k = 1/7

Regarding finding y-intercept, the y-intercept is always the value of the function at x = 0.