Write an equation for the exponential growth. you will still have t as a variable in the equation

Step-by-step explanation:

we know that

The exponential function is of the form

where

y ---> the number of trucks

t ----> is the time in years

a ---> is the initial value (number of trucks for t=0)

b is the base

r is the rate

b=(1+r)

In this problem we have

substitute

we have the point (1,110)

For t=1 year, y=110 trucks

substitute

solve for b

The rate of growth is

the exponential equation is equal to

Verify for the third point of the table

For t=2 years

---->is correct

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.