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

Question

asked Oct 14, 2020 51.0k views

1 Answer

Boden · Answer 1 · 2020-10-19T21:39:25+0000

Answer:

$P(t)=(5)/(2) \cdot (√(2))^t$

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:

$(10)/(5)=(P_0 \cdot a_4)/(P_0 \cdot a_2)$

Simplifying:

2=a^2

Since the base for an exponential function can't be negative then
a=√(2) .

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

$5=P_0 \cdot (√(2))^2$

$5=P_0 \cdot 2$

Divide both sides by 2:

(5)/(2)=P_0

The function is:

$P(t)=(5)/(2) \cdot (√(2))^t$