Question

Find the exponential function that satisfies the given conditions:

Initial value = 37, increasing at a rate of 14% per year

f(t) = 37 ⋅ 14t

f(t) = 14 ⋅ 1.14t

f(t) = 37 ⋅ 0.14t

f(t) = 37 ⋅ 1.14t

Answer 1

f(t) = 37·1.14^t

Explanation:

Without the exponentiation operator, all of the functions you have shown are linear functions, not exponential.

When the increase in a year is 14% = 0.14, it means that the value next year is 1 + 0.14 = 1.14 times the value this year. Since repeated multiplication is signified by an exponent, the multiplier is then ...

... 1.14^t

When t=0, this value is 1.14^0 = 1. You want the initial value to be 37, so you need to multiply this multiplier by 37. The result is ...

... f(t) = 37 · 1.14^t