Question

Find the exponential function that satisfies the given conditions:

Initial value = 67, decreasing at a rate of 0.47% per week

f(t) = 0.47 ⋅ 0.33t

f(t) = 67 ⋅ 1.47t

f(t) = 67 ⋅ 1.0047t

f(t) = 67 ⋅ 0.9953t

Answer 1

a = starting amount = 67

r = rate = 0.47% = 0.0047

t = week

Answer 2

The exponential function that satisfies the given conditions is
`f(t)=67(0.9953)^t`

Solution-

This can be represented as exponential decreasing function,

`f(t)=a(1 - r)^t`

Where,

• a = starting amount = 67
• r = rate = 0.47% = 0.0047
• t = week

Putting the values,

`\Rightarrow f(t)=67(1 - 0.0047)^t`

`\Rightarrow f(t)=67(0.9953)^t`

Therefore, the exponential function that satisfies the given conditions is

`f(t)=67(0.9953)^t`