Give the starting value a the growth factor b and the growth rate r if Q=ab^t=a(1+r)^t Write r as a percent

Question

Q=1750(1.593)^t

a. a=1750

b=1.593

r=0.593

b. a=1750

b=1.593

r=59.3%

c. a=2787,75

b=2.5375

r=0.593%

d. a=2787.75

b=1.593

c=59.3%

Answer 1

The equations above show that

Q = a * b^t

And

Q = 1750 * 1.593^t

By looking at each equation and comparing the two. It is plain to see that

a = 1750

b - 1.593

You cannot multiply a and b together due to the exponent.

Now when introducing the other equation

Q = a(1+r)^t

Substituting the values back we can see that.

a = 1750

1+r = 1.593

-1 -1

r = 0.593

To write r as a percent multiply by 100

0.593 * 100 = 59.3%

Answer 2

By inspection,

a = 1750

b = 1.593

r = b - 1 = 1.593 - 1 = 0.593

As a percent,

r = 59.3%