Question

The average cost of a scientific calculator was $96.50 in 1970. The same type of calculator cost $21 in 2016. Assuming the exponential decay model applies, what will a similar calculator cost in the year 2019? Round your answer tbo the nearest cent.​

Answer 1

Answer: the cost of a similar scientific calculate in 2019 will be $19.01

Explanation:

Given that;

in 1970 cost of S.C = $96.50

in 2016 cost of same calculator = $21

In 2019 cost of a similar calculator = ?

Assuming the exponential decay model applies

dN/dt = -λN

we know that λ is the decay constant

⇒ N(t) = N₀e^-λt

N(t) is price at time t year, N₀ is initial price,

so t = 0 in 1970 thus N₀ = 96.50

also t = 46 in 2016 thus N₄₆ = 21

substituting into our initial expression

N(t) = N₀e^-λt

N(46) = N₀e^-λ×46

21 = 96.50e^-46λ ⇒ In 21/96.50 = -46λ

= -1.5250 = - 46λ

λ = -1.5250 / -46

λ = 0.03315

t = 0 in 1970 thus N₀ = 96.50

also t = 49 in 2019 thus N₄₉ = ?

so

using our initial expression again

N(49) = N₀ e^-49λ

= 96.5 × e^ (-49 × 0.03315 )

= 96.5 × 0.197014404

= 19.01189 ≈ 19.01

therefore the cost of a similar scientific calculate in 2019 will be $19.01