Question

Find the exponential growth model that fits the following two points:

(0,2720) and (8,10225)

Answer 1

The exponential growth model that fits the given points is:

y=2720×(1.392)^x

The exponential growth model can be represented by the equation:

y=ab^x

Given the points (0,2720) and (8,10225), let's plug these values into the equation to form a system of equations:

When

x=0,

y=2720:

2720=ab^0 =a

So,

a=2720.

When

x=8,

y=10225:

10225=2720×b^8

Now, solve for b:

b^8 = 10225/ 2720

b^8 =3.7574

Taking the eighth root of both sides to solve for b:

b= ∛3.7574

b≈1.392

Therefore, the exponential growth model that fits the given points is:

y=2720×(1.392)^x