Question

Find the exponential function P(t)=P0a^t where P(2)=5 and P(4)=10

Answer 1

Answer:

$P(t)=\frac{5}{2} \cdot (\sqrt{2})^t$

Step-by-step explanation:

$P(2)=5$ meants when $t=2$, that the value for $P(t)$ is 5.

So this gives us this equation:

$5=P_0 \cdot a^2$

$P(4)=10$ meants when $t=4$, that the value for $P(t)$ is 10.

So this gives us this equation:

$10=P_0 \cdot a^4$

So I take equation 2 and divide it be equation 1 I get:

$\frac{10}{5}=\frac{P_0 \cdot a_4}{P_0 \cdot a_2}$

Simplifying:

$2=a^2$

Since the base for an exponential function can't be negative then $a=\sqrt{2}$.

So plugging into one of my equations I began with gives me an equation to solve for the initial value,$P_0$:

$5=P_0 \cdot (\sqrt{2})^2$

$5=P_0 \cdot 2$

Divide both sides by 2:

$\frac{5}{2}=P_0$

The function is:

$P(t)=\frac{5}{2} \cdot (\sqrt{2})^t$