Nick started a landscaping company. The function that represents the number of clients Nick has is C(t)=3(2)t, where C is the number of clients, and t represents time in months. Which statement is true?

The growth rate is 3, which means each month, Nick has 3 times as many clients as he had the month before.
The growth rate of Nick's clients is 2% per month.
The initial value is 2, which means that Nick started his business with 2 clients.
The horizontal asymptote is y=0, but it does not mean anything in this situation because Nick starts his company with 3 clients.

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.

answer:

at time x=0 we have 1000, at time x=1 we have 2000, at time x=2 we have 4000.  

so that's an initial value of 1000 and a ratio of 2,

y = 1000 (2^x)

hope this !