The number of bacteria in a lab experiment can be modeled by the function y(t)=270(1.129)^4t. Write an equivalent function of the form y(t)=ab^t. Round your final values to 4 decimal places.
To convert the function y(t)=270(1.129)^4t to the form y(t) = ab^t, we can start by defining a new variable b = 1.129. Then we can rewrite the function as:
y(t) = 270 * (1.129)^4t = 270 * b^4t
Next, we can isolate the exponential term b^t by dividing both sides of the equation by 270 * b^4t:
y(t) / 270 * b^4t = 1
From this equation, we can calculate the value of a:
a = 270 * b^4t
So the equivalent form of the function y(t) = 270 * (1.129)^4t is:
y(t) = a * b^t, where a = 270 * b^4t and b = 1.129
Rounding to 4 decimal places, we get:
a = 270 * b^4t = 270 * (1.129)^4t = 205.3807
So the final equivalent form of the function is:
y(t) = 205.3807 * 1.129^t