Final answer:
The given exponential function y = 400e^(-0.19t) can be rewritten in the form y = 400 * e^(-0.19t).
Step-by-step explanation:
The given exponential function is y = 400e-0.19t. We need to rewrite this in the form y = abt.
First, let's rewrite e-0.19t in the form bt. To do this, we can use the property of logarithms that states ln(ex) = x. Taking the natural logarithm (ln) of both sides, we have ln(y) = ln(400e-0.19t). Using the properties of logarithms, we get ln(y) = ln(400) + ln(e-0.19t). Since ln(ex) = x, the second term simplifies to -0.19t. So we have ln(y) = ln(400) - 0.19t.
Now, we can rewrite ln(y) = ln(400) - 0.19t as y = e^(ln(400) - 0.19t). Using the property e^(ln(x)) = x, we can rewrite this as y = e^ln(400) * e^(-0.19t) = 400 * e^(-0.19t).
Therefore, the function y = 400e^(-0.19t) can be written in the form y = ab^t as y = 400 * e^(-0.19t).
Learn more about Rewriting exponential function in the form y = ab^t