Question

The function f(t) = 5 (4)^t represents the number of frogs in a pond after t years. If this function is graphed, what would be the meaning of the y-intercept?

The pond starts off with 4 frogs




The number of frogs multiplies by 4 each year




The pond starts off with 5 frogs




After the first year, there are 20 frogs

Answer 1

The y-intercept of the function represents the number of frogs in the pond at the beginning, or at year 0.

Step-by-step explanation:

The y-intercept of a function represents the value of the dependent variable when the independent variable is zero. In this case, the function is f(t) = 5(4)^t, which represents the number of frogs in a pond after t years. The y-intercept occurs when t = 0, so we can substitute t = 0 into the function to find the value at the y-intercept:

f(0) = 5(4)^0 = 5(1) = 5

Therefore, the meaning of the y-intercept is that there are 5 frogs in the pond at the beginning, or at year 0.

Answer 2

From my understanding and calculations I got the answer D “after the first year, there are 20 frogs”