Question

Find the values of A and B such that the graph of the exponential function f(t)=A e^{B t} goes through the points (0,5) and (9,4) . [ A=___] [ B=_____]

Answer 1

To find the values of A and B in the exponential function f(t) = A*e^(B*t) that go through the points (0,5) and (9,4), substitute the points into the equation and solve for A and B. A = 5, B = ln(4/5)/9.

Step-by-step explanation:

To find the values of A and B in the exponential function f(t) = A*e^(B*t) that go through the points (0,5) and (9,4), we can substitute these points into the equation and solve for A and B.

Let's start with the point (0,5).

Substituting t=0 and f(t)=5 into the equation, we get:

5 = A*e^(B*0)

5 = A*1

So, A = 5.

Next, let's use the point (9,4).

Substituting t=9 and f(t)=4 into the equation, we get:

4 = 5*e^(B*9)

Dividing both sides by 5, we get:

4/5 = e^(B*9)

Taking the natural logarithm (ln) of both sides, we get:

ln(4/5) = B*9

Dividing both sides by 9, we get:

B = ln(4/5)/9.

Therefore, the values of A and B are A = 5 and B = ln(4/5)/9.